It’s the fall of 2011. Investors are caught up in fears of another 2008-style financial crisis, this time arising out of schisms in the Eurozone. The S&P 500 is trading at 1200, the same price it traded at in 1998, roughly 13 years earlier, despite the fact that its earnings today are almost three times as high as they were back then. The index’s trailing price-to-earnings (P/E) ratio sits at around 12, significantly below the historical average of 16.

Suppose that I’m a hypothetical value-conscious investor who has been taking a cautious stance on the market. I look at the market’s valuation, and think:

“Stocks look cheap here. I’ve been holding all this cash, waiting for an opportunity. Maybe I should get in.”

I then remember:

“Stocks only look cheap because earnings have been inflated by record-high corporate profit margins–10% versus a historical average of 6%. When profit margins revert back to the mean, as they’ve done every time they’ve reached these levels in the past, S&P 500 earnings will shrink from $100 down to $60, lifting the index’s P/E ratio from a seemingly cheap 12 to a definitively not cheap 20.”

With that concern in mind, I hold off on buying stocks, and decide to instead wait for profit margins, earnings and (true) valuations to come back down to normal historical levels.

The year 2012 comes and goes. Profit margins stay elevated, so I keep waiting. 2013 follows–again, profit margins stay elevated, so I keep waiting. 2014 after that–again, profit margins stay elevated, so I keep waiting. Then 2015, then 2016, then 2017–each year I wait, and each year I end up disappointed: profit margins fail to do what I expect them to do. But I’m a disciplined investor, so I keep waiting. During the total period of my waiting, the stock market more than doubles in value, trouncing the returns of my cash-heavy portfolio and leaving me with an ugly record of underperformance.

To evolve as an investor, I’m eventually going to have to be honest with myself: I got something wrong here. Rather than fight that fact, I’m going to need to open up to it and learn from it. I’m going to need to re-examine the potentially mistaken beliefs that brought it about–in this case, potentially mistaken beliefs about the inner workings of corporate profitability.

“I was confident that elevated corporate profit margins would revert to the mean, which is what happened every time they were elevated in the past. But that didn’t happen here. Why didn’t it happen? Where did my analysis go wrong? What did I fail to see?”

These questions are all well and good, but there is a more important question that I’m going to need to ask, a question that often gets missed in post-mortem investigations of this type. Specifically:

“Why did it take me so long to update my beliefs in the presence of repeated disconfirmation? I had a thesis: that the elevated corporate profit margins I was seeing in 2011 would fall back down to past averages. Reality told me that this thesis might be wrong in 2012, when the prediction failed to come true. Then it told me again in 2013. Then it told me again in 2014, and again in 2015, and again in 2016, and again in 2017. Was all of this repetition really necessary? Could I have been more receptive of the message the first time it was presented?”

Winning in the investing game isn’t simply about having true prior beliefs about the world. It’s also about efficiently updating those beliefs in response to feedback from reality. The primary mistake that I made in the above scenario was not the mistake of having incorrect prior beliefs about the likely future direction of corporate profit margins–from the perspective of what I knew in 2011, those beliefs were reasonable beliefs to have. Rather, my primary mistake was my failure to properly update those prior beliefs in response to the steady stream of disconfirmation that kept coming in. The updating process should have moved me to a different stance sooner, which would have allowed me to participate in a greater share of the returns that the market went on to produce.

The Importance of Updating in Investing: Analogy From a Coin-Flipping Game

To better appreciate the importance of updating in investing, we can explore the following investing analogy, expressed in the terms of a coin-flipping game.

Coin-Flipping Game. Suppose that you and a small group of other people are about to compete with each other in a coin-flipping game. Each player will start the game with $1,000 of play money. Rankings in the game will be determined based on how much each player is able to grow that money over the course of the game. At the end of the game, real monetary prizes and penalties will be assigned to players based on where in the rankings they end up.

Two types of coins can be flipped in the game: green coins and red coins. Green coins are physically designed to have a 70% probability of landing heads and a 30% probability of landing tails. Red coins are physically designed to have the opposite profile: a 30% probability of landing heads and a 70% probability of landing tails.

The game is divided into 20 separate rounds, each consisting of 50 coin flips (1,000 flips in total). At the beginning of each round, the game’s referee fills a large bucket with an unknown quantity of red and green coins. He then randomly draws a single coin from it. He uses that coin for all 50 flips in the round, making sure to keep its color hidden from the participants. When the next round comes along, he empties the bucket, refills it with a random number of red and green coins, and draws a coin to use for the ensuing 50 flips.

Before each flip, the referee auctions off “ownership” of the flip to the player that offers to pay the highest price for it. For each bid that a player puts out, other players are given the option of either putting out a higher bid, or stepping aside. If everyone steps aside, then the flip is declared sold.

Once the “owner” of the flip is set, the referee flips the coin. If it lands on heads, he pays out $2.00 in play money to the owner. If it lands on tails, he pays the owner nothing (and therefore the owner loses whatever amount of play money she paid for it). After each round is over, the referee reveals the result of the flip to the participants and opens up bidding for the next flip. The game goes on like this until the end, at which point the final rankings are tallied and the associated monetary prizes and penalties disbursed.

The key to performing well in this game is having an accurate picture of what each flip is “worth.” If you have an accurate picture of what each flip is worth, then you will know when the other players are bidding too little or too much to own it, and therefore you will know whether you should increase your bid and buy it, or stand back and let it be sold.

Suppose that the referee is flipping a green coin in a round. The “worth” of each flip, which we take to be the expected payout to the owner, will be $1.40. In general, you should buy the flip if it’s being offered at a price below this price, and you should refrain from buying it if it’s being offered at a price above it. Of course, any given flip will either land heads and pay out $2.00, or land tails and pay out nothing, so withhindsight you will be able to say that a given flip was a good buy even though it was priced above $1.40, or that it was a good sell even though it was priced below it. But in this game you don’t have the luxury of making decisions in hindsight. All you can do is look forward. If you do that, you will realize that over a large number of flips with a green coin, heads will tend to occur 70% of the time, and tails 30% of the time. The payout per flip will therefore tend to average out to: 0.70*($2.00) + 0.30*($0.00) = $1.40, which is the highest price that you should generally be willing to pay. By the same logic, if it turns out that the referee is flipping a red coin in a round, then the expected payout to the owner of each flip, which we take to be it’s “worth”, will be: 0.30*($2.00) + 0.70*($0.00) = $0.60. If the coin is red, then you generally should be willing to buy a flip up to that price, but not above it.

(Note: There are other considerations, beyond the mere “worth” (expected payout) of a flip, that may prove relevant to your decision of how much to bid for it. If you know that other players are likely to try to outbid you, you might want to continue to place bids even after the price has risen above your estimate of the worth, purely in order to force those players to pay higher prices. You might also become rationally risk-seeking, in the sense that you’re willing to buy flips at prices above their worth precisely because you’re looking for a “gamble”–consider, for example, a scenario near the end of the game in which the person directly ahead of you in the rankings is only slightly ahead, but the person directly behind you is very far behind. In that case, you might have a lot to gain and nothing to lose from a gamble, so you may be willing to take it even at odds that are against you. Finally, given that your expected return from buying a flip will depend on the difference between the worth and the price you pay, you will technically need to stop bidding when the price is some distance below the worth, so that your expected return stays positive, and also so that you are able to conform with the Kelly Criterion. That necessary distance will usually be tiny, but it could become significant, depending on how much money you have left in the game. These considerations, while interesting, are beyond the scope of what we’re trying to explore here.)

To form an accurate picture of what each flip in the game is worth, you’re going to need to find out whether the referee is using a green coin or a red coin for the flip. Unfortunately, you can’t directly find that out–he’s intentionally keeping it a secret from you. However, you might be able to assign a probability that he’s using a green coin or a red coin in any given round based on other information that is available to you. Combining that probability with the probability that each type of coin will land heads or tails will allow you to build a second-order estimate of the worth of each flip. That estimate will be some number between $0.60 (the worth of a red flip) and $1.40 (the worth of a green flip), scaled based on how likely you think it is that the referee is flipping one type of coin versus the other.

So that’s where the real challenge in the game lies. You need to do a better job than the other participants of using available information to form a second-order estimate of the worth of the various flips that are taking place. If you can do that, then over time and across many different rounds and flips, you will tend to buy at better prices than the other participants, which will allow you to earn more money than they earn. It’s in this sense that the game represents an apt analogy to investing. The challenge in investing is the same challenge: to do a better job than the rest of the market of using available information to form an estimate of the likely returns of the various investment securities that are on offer, across whatever time horizon you happen to be focusing on. If you can do that, then over the course of many different investment periods, you will tend to invest in securities that produce better returns than the average, which will cause you to outperform the “market.”

Returning to the game, to proceed intelligently in it, you’re going to need to be given information to use. So let’s assume that at the beginning of each round, after the referee draws his coin, he lets you and the other participants dig around inside the bucket to determine how many green coins are in it versus red coins. Knowing how many green coins are in the bucket versus red coins will allow you to assign a probability to the prospect that he drew a green coin or a red coin, given that he randomly drew the coin from the bucket.

To clarify, there are two different senses of “probability” that we’ve been using here. The first sense is the frequentist sense, in which “probability” is taken to refer to the frequency at which something will tend to happen over a large number of trials. For example, over a large number of flips, green coins will tend to fall on heads 70% of the time, and red coins will tend to fall on heads 30% of the time, so we say that green coins have a heads probability of 70%, and red coins have a heads probability of 30%. The second sense is the Bayesian/Laplacian sense, where “probability” is taken to refer to our degree of belief in something. For example, suppose that I count the coins in the bucket and determine that there are 9 green coins for every one red coin. The referee drew his coin from the bucket. If he drew it randomly, without preference, then I can say that there’s a 9 out of 10 chance, or a 90% probability, that he drew a green coin. But this number only reflects my degree of belief that he drew a green coin–in reality, the matter has already been settled, he either drew a green coin or he didn’t. These two senses of the term may seem incompatible, but they need not be. In fact, if Laplace is right that the universe is deterministic, then they will essentially reduce to the same thing. All perceived randomness in the world will simply be the result of ignorance.

Suppose that prior to the start of the first round of the game, you dig around in the bucket and come to estimate that roughly 90% of the coins in it are green and that roughly 10% are red. From your perspective, this means that there’s a 90% chance that the referee drew a green coin, and a 10% chance that he drew a red one. Combining those probabilities with the green coin’s 70% heads probability and the red coin’s 30% heads probability, your new second-order estimate of the worth of each flip in the round will be 0.90*0.70*$2.00 (case: coin is green, referee flips heads) + 0.10*0.30*$2.00 (case: coin is red, referee flips heads) = $1.32.

Let’s now start the first round of the game. For the first flip, you’re able to successfully buy it for $1.20, which is an attractive price from your perspective, below your worth estimate of $1.32. The result of the flip comes back “Tails”, so you lose $1.20. On the next flip, you’re again able to successfully buy it at $1.20. The result of the flip again comes back “Tails”, so you again lose $1.20. Eight more flips follow. In each case, you successfully outbid the rest of the market, buying at $1.20. The results of the flips come back TTHTTTTH. After ten flips, the result then stands at 2 heads and 8 tails, leaving you with a cumulative loss of $8.00. Ouch.

You begin to wonder: if the coin is, in fact, green, i.e., 70% biased to land heads, then why is it landing so much on tails? Uncomfortable with the situation, you pause the game to investigate. It seems that you are being confronted with two possible outcomes, both of which are unlikely, and one of which must have actually taken place.

Outcome #1 — The Referee Drew a Red Coin: You determined that the bucket contained 9 green coins for every one red coin. On that basis, there was a 90% chance that when the referee drew the coin for the round, he drew a green coin. Did he, in fact, draw a red coin? It’s possible, but unlikely.

Outcome #2 — The Referee Drew a Green Coin but, by Chance, the Flip Results Have Come Back Tails-Heavy: If the first unlikely outcome did not take place–that is, if the referee is, in fact, flipping a green coin as initially expected–then a different unlikely outcome will have taken place. Specifically, the referee will have conducted 10 flips of a coin with a 70% chance of landing heads, and the coin will only have landed heads twice–20% of the time. The flipping process has an element of random chance to it, so this outcome is possible. But it’s unlikely.

What you have, then, are two unlikely possible outcomes, one of which actually happened. To properly “update” your beliefs about what color of coin the referee is likely to be using, you’re going to have to weigh these two unlikely possible outcomes against together. The correct way to do that is through the use of Bayes’ Theorem, which we will now take a detour into to explain. Readers that are already fresh on Bayes’ Theorem can feel free to skip the next section–but let me say that I think the explanation that I give in it is a pretty good one, likely to be worth your time, even if you’re already strong on the topic.

Bayes’ Theorem Explained

Bayes’ Theorem expresses the following relationship:

P(H|D) = P(D|H) * P(H) / P(D)

We can think of the letter H here as referring to some hypothesis or belief, and the letter D as referring to some data or information that is obtained subsequent to that hypothesis or belief. Bayes’ theorem tells us how to “update” the probability that the hypothesis or belief is true in light of the data or information that has been obtained. The intuitive basis for the theorem is difficult to grasp, and even more difficult to retain in memory in a clear form. To help make it clear, I’ve concocted the following spatial analogy.

Imagine a square of area 1, shown below. Inside the square is a circle H of area P(H). Ignore the weirdness of the term P(H) for a moment–just assume that it’s a number representing an area. You’re standing above the square with a single speck of sand on your finger. You flick the speck down onto the square. It lands somewhere inside the square. You don’t know where that is because the speck is too small to see from a distance. It could be anywhere.

The question we want to ask is, what is the probability that the speck is inside circle H? Given that it was flicked onto a random spot inside the square, the answer has to be: the area of H, denoted by P(H), divided by the area of the square, which is 1. Think about that for a moment and you will see why it has to be true: the only factor that can impact the probability that a randomly located speck is inside a given space is the area of the space. P(H) / 1 = P(H), so the probability that the speck is inside H is simply P(H).

Now, suppose that I draw another circle inside the square and label it circle D, with an area of P(D). I then reveal to you that when you flicked the speck onto the square, it landed somewhere inside circle D. To repeat, the speck of sand is located somewhere inside circle D–you now know this for a fact.

The question then becomes, knowing that the speck is located somewhere inside circle D, how does your estimate of the probability that it is inside circle H change? In other words, what is the probability that the speck is inside H given that it is known to be somewhere inside D? The way we express this latter value is with the term P(H|D), which means the probability of (the speck being in) H given (that we know the speck is in) D.

Intuitively, we can see that the value of P(H|D) is simply the area of the overlap between circle H and circle D, which we label as P(H&D), divided by the area of circle D, which is P(D).

Expressing this intuition formally, we get at a simplified version of Bayes’ Theorem:

P(H|D) = P(H&D) / P(D).

What the theorem is saying is that the probability of (the speck being in) H given (that the speck is in) D is equal to the area of overlap between H and D (denoted by P(H&D)), divided by the area of D (denoted by P(D)).

Notice that if the area of overlap between H and D is small compared to the area of D, then the probability of (the speck being in) H given (that the speck is in) D will be low (see left schematic). And if the area of overlap between H and D is large relative to the area of D, then the probability of (the speck being in) H given (that the speck is in) D will be high (see right schematic).

To make the theorem useful for quantitative applications, we incorporate the following equality:

P(H&D) = P(D|H)*P(H)

To understand this equality, recall that P(H&D) is the probability that the speck is inside both H and D. Intuitively, that probability is equal to the probability that the speck is inside H–which is P(H)–times the probability that it is inside D given that it is inside H–which is annotated P(D|H).

Substituting the above equality into the simplified version of the theorem, we arrive at the more familiar version, presented at the beginning of the section:

P(H|D) = P(D|H)*P(H) / P(D)

In Bayesian applications, the term P(H) is called the “prior probability.” It’s the initial probability that we assign to our hypothesis being true. Subsequent to that assignment, we will receive data with implications for the truth of the hypothesis. The term P(D|H), called the “likelihood function”, expresses how likely it is that we would receive that data assuming that the hypothesis is true. To “update”, we multiply the prior probability times the likelihood function. We then divide by P(D), sometimes referred to as the “normalizing constant”, which ensures that a measure of 1 is obtained across the overall probability space.

Our “speck of sand” analogy provides a useful intuitive illustration of how the process of Bayesian updating works. We start with a hypothesis: that the speck of sand is located inside circle H (note that we chose the letter ‘H’ to symbolize ‘hypothesis’). We assign a prior probability P(H) to that hypothesis being true. It is then revealed to us that the speck of sand is located inside a second circle, D. This fact obviously has implications for our hypothesis–it is relevant data, which is why we labeled the circle with the letter ‘D’. Upon receiving this data, we update the probability that the hypothesis is true to be a new number. Specifically, we set it to be equal to “the area of overlap between H and D” divided by “the area of D.” Intuitively, that’s what it immediately changes into, once we know that the speck is inside D.

To extend this “speck of sand” intuition to broader applications, we need to understand that for any data that we obtain subsequent to a hypothesis, the hypothesis will exhibit some “overlap” with the data, which is to say that the truth of the hypothesis will represent one possible pathway through which that data might have been obtained. To estimate the probability that the hypothesis is true given that the data was obtained, we need to quantify how prevalent that pathway is relative to all pathways through which the data could have been obtained, including alternative pathways that conflict with the hypothesis. That is what Bayes’ theorem does.

The Dangers of Overconfidence

To return to the coin-flipping game, recall that you were struggling with a dilemma. On the one hand, after digging through the bucket, you estimated that 9 out of 10 coins in the bucket were green, and therefore that there was a 90% chance that the referee, who randomly drew his coin from the bucket, was using a green coin. On the other hand, after several rounds of the game, you noticed that a string of tails-heavy results had been accumulating, an outcome that you would not have expected to see if a green coin were being used. The solution to this dilemma is to update your initial estimate of the probability that the referee is using a green coin to reflect the implication of the tails-heavy result that you’ve since observed.

In truth, you should have been doing that the entire time–the fact that you weren’t is part of the reason why you’ve been losing money in the game. Recall that the coin-flipping game, like the game of investing, is ultimately a game about who is able to do the best (most efficient, most accurate) job of using available information to build an estimate of what things are worth. Here, “available information” isn’t limited to your “prior”, i.e., your initial estimate of the probability that the referee was using a green coin. It also includes the actual results of the flips that have been accumulating since the round began–those results contain valuable information about what type of coin the referee is likely to be using, information that you cannot afford to ignore.

The table below shows what a proper updating process would look like during the round, assuming that we start out with 90% confidence (prior) that the coin is green. The two important columns in the table are “Rnd Gen (H/T)”, which shows the cumulative results of the flips in the round, and “Updated Worth ($)”, which shows how our estimates of the worth of each flip evolve in response to them.

Assuming that the referee has, in fact, been using a red coin with a 30% heads probability (the assumption that we used to generate the above data), it will take our updating process around 9 flips to sniff that fact out. After those nine flips, our worth estimate will have effectively converged onto the correct value of $0.60, even though we started the process with a belief that was incorrect.

To summarize, the proper way to play each round of the game is as follows:

(1) Assign a prior probability to the hypothesis that the referee is using a green (or a red) coin, and use that probability to calculate the worth of each flip. To assign a good prior probability, we need information. There are many ways to get it. We can sample the contents of the bucket and use the observed ratio of green coins to red coins to infer a probability, which is what the referee was allowing us to do. We can study the bidding patterns of the other participants, which might contain valuable clues as to the color of coin being used. We can install hidden cameras in the place where the flips are being conducted, which will allow us see the color of the coin for ourselves. We can try to convince insiders who know what color the coin is to reveal that information to us. We can even pay the referee to tell us the color directly. Any piece of information will potentially be valuable here, if it can improve our estimate of the probability that the referee is using a given type of coin.

(2) Update that probability as actual coin flip results accumulate. For this, we use Bayes’ Theorem.

If we’re more efficient and accurate in performing (1) and (2) than our fellow participants, then over many rounds and many flips, we will tend to earn more money than they earn. The same is true in the game of investing.

Now, suppose that we’re in a new round where a red coin is actually being used, but we initially think it’s likely to be a green coin. The following chart shows how our estimates of the worth of each flip will evolve in that case. The different lines show the different worth estimates that we would arrive at using different prior green coin probabilities: 0.500 (no idea), 0.900 (likely green), 0.990 (very likely green), and 0.999 (virtually guaranteed to be green). The correct worth estimate, of course, is $0.60, because the coin is, in fact, red. By updating properly, we will eventually get to that estimate, on each of the assumed priors. The difference, of course, will be in how many flips it will take for us to get there, and how much we will lose in the interim period from our resulting willingness to overpay.

(Note: Y-axis is the worth estimate, X-axis is the flip number in the round. Each line begins after the results of the first flip, so the first worth estimate is already an updated number.)

Notice that if we assign a 0.500 prior probability (blue line) to the coin being green, which is a way of expressing the fact that we have no information about the coin’s likely color, and the coin ends up being red, we may still do OK in the round. That’s because the updating process will efficiently bring us to the correct worth estimate, even though we’ll be starting from an incorrect estimate. The process won’t take long, and our worth estimates won’t spend too much time at values far away from the true worth.

But if we assign higher probabilities to the coin being green–say, 0.990, or 0.999, per the above–and the coin ends up being red, our performance in the round is going to suffer. The updating process that will be needed to move us to a correct estimate will end up taking significantly longer, and we’ll be significantly overpaying for each flip along the way. The reason that the updating process will take significantly longer on these more confident priors (0.990, 0.999, etc.) is that a large number of unexpected tails will have to accumulate before the ensuing result will be “unlikely” enough (on a green coin) to outweigh our strong green coin priors and sufficiently alter our stance. Each one of the tails that has to build up will come at a cost–a substantial cost, given how far off our worth estimates (and our bids) are going to be.

To see the inefficiency play out, consider the performance of the 0.999 prior, shown in the purple line above. That prior corresponds to an assigned 99.9% probability that the coin is green. Even after 10 flips, where 80% come back tails, we’re still going to be assigning a very strong probability to the coin being green–93.5% to be exact. Our estimate of the worth will have hardly budged, sitting at roughly $1.35, in comparison with the actual worth of $0.60.

The next chart shows how our estimates of the worth of each flip might proceed in a round in which a green coin is used.

As in the previous case, the blue line, which is the worth estimate that we arrive at using a 0.500 prior (no knowledge either way), starts out at an incorrect value (technically $1.00, though the chart begins after the first update, when the estimate is roughly $1.18). Despite this incorrect starting point, the estimate quickly converges onto the right answer ($1.40) through the updating process. We can’t really see the green line, the red line, or the purple line because they essentially start out on the correct worth estimate from the get-go, at values close to $1.40. “Updating” them ends up not really being required.

The contrast between these cases highlights the asymmetric risks associated with overconfidence in the game. If we assign a very high prior probability to the coin being green–a highly aggressive number such as 0.999–and the coin ends up being red, we’re going to retard the updating process and create significant losses for ourselves. At the same time, if we assign that number and the coin ends up being green, we aren’t going to gain that much in efficency or accuracy relative to what less aggressive assignments might have produced. Now, to be fair, this apparent risk asymmetry is a corollary of the fact that if we are actually correct in assigning a high prior probability to the coin being green, then a situation where it ends up being red isn’t going to happen (except maybe once in a blue moon). But if it does end up happening more often than that, suggesting that we were too confident in our assignment, we’re going to pay a heavy price for the mistake.

Now, I want to be clear. If we’re genuinely confident that the coin is green, then we should assign a strong prior probability to it and calculate the worth of each flip accordingly. That’s how we’ll win the game. But we need to make sure that we have a sound basis for our confidence. If our confidence turns out to be unfounded, such that we end up assigning a high prior probability to the wrong color, it’s going to be significantly more difficult, mathematically, for us to “update” back to the right answer. Our strong prior is going to effectively tie us down into believing that the coin is the color we initially thought it was, even as the incoming evidence screams otherwise.

Insights for the Profit Margin Debate

The primary mistake that those who were bearish on profit margins made in earlier phases of the current market cycle–and I would have to include myself in that group, at least for a time–was not the mistake of having “wrong” beliefs about the subject, but rather the mistake of assigning too much confidence to those beliefs. There wasn’t a sound basis for being confident in them, first because the subject itself was inherently murky, and second because the arguments that were being used were of types that tend not to be reliable (the arguments may have been persuasive, but persuasive and reliable are not the same thing).

Looking specifically at the theoretical arguments, those who were bearish on profit margins argued that competition would eventually force a mean-reversion to occur. But what competition were they talking about? Competition where? In what sectors? Among what companies? Competition has always been around. If it represented the antidote to elevated profit margins, then why had it allowed profit margins to become elevated in the first place? If it was capable of reversing them, then why hadn’t it been capable of stopping them from forming?

Abstract theoretical arguments such as the one presented above tend to miss important details. Granular examinations, conducted rigorously from the bottom up, are usually more reliable. If such an examination had been conducted in this case, it would have shown that the profit margin expansion that took place from the mid 1990s to 2011 was not broad-based, but was instead concentrated in select large-cap companies, most notably those in the Tech industry (think: companies like Apple, Microsoft, Google, etc). Inside specific sectors, the profit margin expansion was skewed, with companies in the highest tiers of profitability seeing large profit margin increases, and companies in the lower tiers seeing no increases at all, or even decreases. These are exactly the kinds of signs that we would expect to see if increased monopolization were taking place in the competitive landscape. Something appears to be making it easier for large best-of-breed corporations, particularly those in the Tech sector, to earn high profits without being threatened by competition. Whatever that something is (and it is likely to be multiple things), there was little reason to be confident, in 2011, that it was about to go away.

Looking specifically at the empirical arguments, those who were bearish on profit margins pointed out that every time profit margins had been at current levels in the past, they had always eventually fallen back down to the mean. But what was the sample size on that observation? Two historical instances? Three? Maybe four? A hypothesis inferred from a small sample may be worth embracing, but it should be embraced with caution, not confidence. And what about the data from the mid 1990s to 2011, data that, with the exception of brief recession-related drops in 2001 and 2008 (both of which quickly reversed themselves), had been showing a clear and persistent tendency towards profit margin elevation? This is what the chart of profit margins looked like from 2011’s vantage point:

If the goal was to accurately predict what was going to happen from 2011 onward, then the data from the mid 1990s to 2011 should have been weighted more heavily than data from more distant periods of history, given that that data was obtained from a period that was temporally closer to (and therefore more likely to share commonalities with) the period of interest.

Granted, it’s easy to make these points in hindsight, given that we know how the result ended up playing out. But I would nonetheless maintain that a sound evaluation of the theoretical and empirical evidence for the mean-reversion hypothesis, carried out from the perspective of what could have been known at that time, would have led to the assignment of significant uncertainty to the hypothesis, even if the hypothesis would have been retained. If that uncertainty had been appreciated, the updating process would have been completed more quickly in response to the disconfirming results that ensued, which would have allowed those investors who initially embraced the hypothesis to have participated in a greater share of the returns that the market went on to deliver.

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In this piece, I’m going to share a mental exercise that we can use to increase the truthfulness of our thinking. The exercise is intended primarily for traders and investors, given their obvious (financial) reasons for wanting to think more truthfully about the world, but it has the potential to be useful for anyone in any field who has that goal.

Background: Motivated Cognition

As intelligent human beings, we have the ability to be truthful, i.e., to recognize and communicate the truth. We use that ability whenever we make genuine attempts to see and describe the world correctly, as it actually is. Unfortunately, our mental processes tend to be compromised by a phenomenon called “motivated cognition.”

Motivated cognition refers to our unconscious tendency to selectively process information in ways that suit ends or goals unrelated to the truth. Examples of such ends or goals include: (1) protecting our own interests (or the interests of those that are tied to us or that we see as being similar to us in some way), (2) sustaining positive images of ourselves and preserving or status and reputations in communities, (3) avoiding antagonism with others, particularly those whom we like or draw benefits from, (4) weakening the positions of those whom we dislike, distrust or view as threats, and (5) insulating ourselves from realities that, if acknowledged, would create dissonance in our values and commitments.

In many areas of life, our tendency to engage in motivated cognition benefits us. That’s not a surprise–if it didn’t benefit us, then it would never have evolved as a tendency in our species. The reason that it can benefit us, even as it moves us away from the truth, is that, in many areas of life, the truth doesn’t enforce itself. It doesn’t impose consequences on those who go against it. Examples of such areas include: politics, media, sales, entertainment, law, religion, and so on. In these areas, appearances tend to be more important than reality. Outcomes tend to be decided by the question of who does the best job of persuading people and of favorably impacting their feelings, not by the question of who makes the truest statements about the world.

But there is one area of life, near and dear to all of our hearts, where the truth does enforce itself, imposing severe consequences on anyone who dares to go against it. That area is the area of speculation. To “speculate” is to put something of value–usually money, but it can be other things–directly at risk on a belief. When a person speculates, she makes herself fully accountable to the truth. If she speculates correctly, in accordance with the truth, she gains a reward. If she speculates incorrectly, in opposition to the truth, she suffers a punishment. These incentives serve to sharpen her focus on the truth. They cause her to actually care about whether her descriptions of the world are correct. With real consequences at stake, she finds herself closely examining the evidence, carefully checking her reasoning, and taking seriously the possibility that she might be wrong–things that she is not as likely to do in other areas of her life.

A simple way to force our thinking to be more truthful, then, is to tie it to an act of speculation–not necessarily in the literal sense of placing actual bets on our beliefs, but in the imaginary sense of envisioning ourselves having to place bets on them, and observing how our stances change. For any issue that we might be confronted with, if we want to get ourselves to think about the issue in a more truthful way, free from the emotional biases and distracting incentives that tend to lead us astray, what we need to do is imagine ourselves in a situation where we are forced to speculate on it, with real consequences to be decided by whether we speculate correctly. In that state of mind, truth will become our primary focus.

Entering a Truth Chamber

To frame the point in a more vivid way, suppose that there is some question that we want to get ourselves to think about in a more truthful way. We can accomplish this by imagining something like the following:

(1) There is a way to conclusively resolve the question–for example, some perfect set of experiments or tests that we can conduct to get the answer, or an all-knowing God that can reveal it to us. The details don’t really matter here–what matters is that we know that we’re going to get the answer, and we know that when we do get it, any doubts that we or anyone else might have had about it will be eliminated. (Note: if it is hard to envision the question having a conclusive answer, then either it is not being framed precisely enough and needs to be reframed, or it is about certain types of subject matter–for example, moral claims and judgments of value–that do not purport to describe any actual reality and that reality therefore cannot answer).

(2) We are taken into a private booth to cast a vote on the question. Crucially, we are promised that no one will ever be able to see or know how we voted–not even our future selves, because our short term memories of the process will be erased. We posit this privacy condition in order to eliminate the possibility that our vote might be influenced by the anticipation that others will praise or shame us for it, or the concern that we ourselves will come to regret it. None of that will happen because no one, not even our future selves, will ever have a way to know how we voted.

(3) We are asked to specify things that we value in life and that we want more of–for example, money, resources, relationships, health, activities, leisure, achievement, respect, enjoyment, insight, peace of mind, beauty, admiration, something for others, something for the world, whatever. We are told that, if we vote correctly on the question, we will be given these things, in whatever amount or combination we need to be genuinely happy. And if we vote incorrectly, we will either receive nothing, or we will face a punishment, which could range from something negligible (e.g., loss of a trivial amount of time or money) to something extreme (e.g., imprisonment, torture). As designers of the scenario, we would set the severity of the punishment based on how much urgency we want to inject into the exercise. Note that the more severe we set the punishment, the more anxiety we will be introducing into the deliberation, which can have the effect of clouding our judgment. We want to set the stakes at a sweet spot: enough to be a big deal to us and to motivate us to aggressively seek out the truth, but not so extreme as to overwhelm us with stress and impair our ability to think clearly. For me, that sweet spot is probably: lots of wonderful things if I answer correctly, and a small loss of some money if I answer incorrectly.

On the basis of these imagined assumptions, we proceed to ask ourselves two questions. First, which way would we vote on the question? The answer tells us which side of the question we think is most likely to be true. Second, how much wavering, vacillation and uneasiness would we experience in casting that vote? The answer tells us how confident we are in our vote–and, by extension, how much uncertainty we should attach to our associated beliefs on the matter.

I refer to the hypothetical place that this exercise puts us in as a “Truth Chamber”, because being in it is like being in one of those sound-proof chambers used for hearing tests, which block out all background noise and allow us to detect tiny sounds that we otherwise wouldn’t notice. Entering a “Truth Chamber” blocks out all of the ulterior motivations that influence our cognition, and puts everything that we value at stake on the accuracy of our thinking. Unsurprisingly, in that setting, we become laser-focused on the truth, laser-focused on describing reality as correctly we possibly can. Instead of settling on the usual path of least resistance, which is to lazily embrace whatever conceptions of the world best fit with our interests and preferences, we find ourselves inquiring, questioning, searching, exploring, checking, challenging, and so on, all with the goal of increasing our chances of successfully arriving at the truth. In everyday life, outcomes tend to hinge on appearances and superficialities, and arriving at the truth doesn’t really matter. In a Truth Chamber, arriving at the truth is the only thing that matters, and it matters immensely.

Test Cases: Dangerous Ideas

In an excellent article from a few months ago, the well-known cognitive scientist Steven Pinker introduced a series of questions centered on what he referred to as “Dangerous Ideas”–ideas that could very well be true, but that we find inappropriate, offensive, threatening, and immoral. These questions represent good test cases for us to use in experiencing the mental “shift” that takes place when we approach questions truthfully, from the perspective of being inside a Truth Chamber.

So, pick a few questions from the article excerpt below, re-frame them as needed to make them sufficiently precise and tractable, and compare the different experiences that you have in trying to decide on answers for them (1) normally, without facing any consequences, and (2) from the perspective of being inside a Truth Chamber, where your entire future will hinge on whether you are able to answer them correctly, in accordance with the actual truth. Remember that even if you are not certain on the answer to a question, you still have to cast vote. It is therefore in your interest to take a probabilistic approach, choosing the answer that seems most likely to be true, given what you know.

Do women, on average, have a different profile of aptitudes and emotions than men? Were the events in the Bible fictitious — not just the miracles, but those involving kings and empires? Has the state of the environment improved in the last fifty years? Do most victims of sexual abuse suffer no lifelong damage? Did Native Americans engage in genocide and despoil the landscape? Do men have an innate tendency to rape? Did the crime rate go down in the 1990s because two decades earlier poor women aborted children who would have been prone to violence? Are suicide terrorists well educated, mentally healthy, and morally driven? Are Ashkenazi Jews, on average, smarter than gentiles because their ancestors were selected for the shrewdness needed in money lending? Would the incidence of rape go down if prostitution were legalized? Do African American men have higher levels of testosterone, on average, than white men? Is morality just a product of the evolution of our brains, with no inherent reality? Would society be better off if heroin and cocaine were legalized? Is homosexuality the symptom of an infectious disease? Would it be consistent with our moral principles to give parents the option of euthanizing newborns with birth defects that would consign them to a life of pain and disability? Do parents have any effect on the character or intelligence of their children? Have religions killed a greater proportion of people than Nazism? Would damage from terrorism be reduced if the police could torture suspects in special circumstances? Would Africa have a better chance of rising out of poverty if it hosted more polluting industries or accepted Europe’s nuclear waste? Is the average intelligence of Western nations declining because duller people are having more children than smarter people? Would unwanted children be better off if there were a market in adoption rights, with babies going to the highest bidder? Would lives be saved if we instituted a free market in organs for transplantation?

Understandably, we have certain visceral reactions to these questions, and we’re inclined to want to say certain things in response to them. But when we entertain them from the perspective of being inside a Truth Chamber, a shift takes place. We realize that in answering them, we are no longer answering to our peers, to society, to ourselves, or to our values. We are answering to reality, an entity that simply is what it is and that doesn’t care about anything. Our focus therefore turns entirely to the truth, to describing that reality as correctly as we possibly can. We find ourselves asking questions such as:

“What’s likely to be the actual truth with respect to this question? Not what I want to be true, but the actual truth–what’s it likely to be?”

“Do I really know that? Am I sure? Could I be overreacting to something, or underreacting to something, or ignoring something, or suppressing something, or missing something important?”

“What do I have right now, in terms of evidence, to support my answer? Is the kind reasoning that I am using to get to that answer actually reliable?”

“What information can I go look at to get a better picture of the actual truth about this subject?”

The most important question that the exercise provokes is this last one. The exercise causes us to realize that, at this moment, we probably don’t know enough to reliably give answers to any of these questions, and that if we want to have strong views on them, we would be well-served by going out and doing more research. Importantly, our goal in conducting such research would not be what it normally is–i.e., to justify the answers that we’ve already committed to, so that we can “win” the debates that we’re having with our opponents on the question. Rather, our goal would simply be to get to the right answer, the correct answer, the true answer, whatever that answer happens to be. This is what it means to be truthful.

How the Exercise is Intended to be Used

I’m now going to offer some important clarifications on how the exercise is intended to be used.

First, the idea behind the exercise is not for you to literally walk through it, in full detail, every time you are confronted with a question that you want to think more truthfully about. Rather, the idea is simply for you to use it to get a sense of what it feels like to be genuinely truthful about something, to genuinely try to describe something correctly, as it is, without pretenses or ulterior motivations. If you know what that state of mind feels like, if you are familiar with it, then you will be able to stop and return yourself to it as needed in your trading and investment deliberations and in your everyday life, without having to actually step through the details of the scenario.

Second, the exercise is intended to be used in situations where you actually want to get yourself to think more truthfully about a topic and where you would stand to actually benefit from doing so. Crucially, that situation does not describe all situations in life, or even most situations. There are many situations in life where extreme truthfulness can be counterproductive, creating unnecessary problems both for you and for others.

Third, all that the exercise can tell you is what you believe the most likely answer to a question is, along with your level of confidence in that belief. It cannot tell you whether you are actually correct in having that belief. You might believe that the answer to a question is X when it’s in fact Y; you might have a lot of confidence in your belief when you should only have a little. Your understanding of the subject matter could be mistaken. You could lack the needed familiarity or experience with it to have a reliable opinion. Your judgment could be distorted by cognitive biases. These are always possibilities, and the exercise cannot protect you from them. However, what it can do is make you more careful and humble as a thinker, more open to looking inward and assessing the strength and reliability of your evidence and your reasoning processes, more willing to update your priors in the face of new information–all of which will increase your odds of getting things right.

Fourth, the exercise is not intended to be used as a tool to “win” debates against other people–i.e., to encourage lines such as “You would never say what you are saying right now if you had to bet money it!” Rather, it’s intended to be used as a tool to allow you to more clearly recognize what you consider to be most likely to be true, when you are being fully honest with yourself. It’s a private thing, not a public thing.

(On a side note, the concept of “motivated reasoning” has become very popular in intellectual discourse. I’ve seen a number of instances of people attempting to use it to attack the positions of those they disagree with: “Psychologists talk about this thing called motivated reasoning, and that’s exactly what you’re doing right now!” But in a debate, pretty much everyone is engaging in motivated reasoning, selectively searching for arguments and evidence to bolster conclusions that they’re emotionally attached to. It’s disingenuous for one side to “play the psychologist” and call out the other side out on it.)

Application: Quantitative Easing

At this point, I anticipate that at least some readers will have the following reaction to what I’ve said so far:

“This is all great, but why do traders or investors, in particular those that put their own money at risk, need any of it? They already have a financial incentive to be truthful in their speculative activities, so what are they going to gain from an imaginary speculation-based exercise designed to increase that?”

The answer is that traders and investors are just as exposed to emotional biases and distracting incentives as everyone else. Like everyone else, they don’t like to confront unwanted realities, or abandon prior commitments, or admit to past mistakes, or acknowledge personal shortcomings, or embark on stressful changes of course, or accept perceived “defeat” in their disputes with their intellectual adversaries. The hope, of course, is that the monetary skin that they have in the game would be sufficient to get them to be willing to do all of those things, given what is at stake. But not all traders and investors have their own money in the game–most speculate primarily with other people’s money. For those individuals, the primary incentive is not performance per se, but maintaining the confidence of the investor base, a game that depends more on appearance and persuasion than on actual truth. And for those that do have their own money in the game, money is just money, it isn’t everything. If we want to reliably force ourselves to be truthful and honest a subject matter we are investigating, we need to imagine having more important things than money at stake–e.g., our well-being, our happiness, our freedom, etc. Only then will the quest for truth become sufficiently urgent to get us to diligently prioritize truth over the other forces tugging on us.

To conclude the piece, I’m going to illustrate the potential application of the exercise by using it on myself. To that end, consider the following contentious macroeconomic claim:

Claim: “The Federal Reserve’s third quantitative easing program (QE3), implemented at the end of 2012, provided a meaningful positive contribution to the performance of the United States economy from that date onward.”

(Note: Quantitative easing is a macroeconomic policy wherein a central bank creates new money and uses it to purchase existing financial assets in an economy–for example, already-issued government bonds. In most cases, the result of the policy is an increase in the broad money supply, but there is typically no net increase in the total quantity of financial assets in the system, because the money that the central bank puts into the system is offset by the financial assets that the central bank takes out of it.There is a contentious debate among economists as to the extent to which this policy is capable of stimulating economic activity, and under what circumstances.)

If you ask me whether the claim is true or false, I’m going to want to say that it’s false–that QE3, given its timing in 2012, provided a negligible contribution to growth, if any at all. But if I’m being honest, I have to admit that my inclination to say this is at least partially rooted in subtle emotional considerations that have nothing to do with whether the claim itself is correct. Specifically:

In the late summer and fall of 2010, when the Federal Reserve (Fed) started giving out hints that it was going to embark on a second QE program, the market rallied. I was positioned bearishly at the time, and instead of responding appropriately to what was happening, I entrenched in my bearish stance, missing out on sizeable market gains. The experience left a bitter taste in my mouth, and made me somewhat averse to the concept of Fed intervention. It’s a fairness thing–intervention represents a sneaky and self-serving “changing of the rules” in the middle of the game, and is unfair to those speculators who get caught on the wrong side of it. I empathize with that point of view because I was once one of those speculators. (To be clear, this is an emotional thing. On a rational level, I see how silly it is. The central bank is no different from any other market force that speculators are tasked with anticipating and responding to. Speculators who ignore or miscalculate it have failed to do their jobs and deserve whatever losses they incur).

To say that quantitative easing works to stimulate an economy is to say that the Fed is justified in using it. I don’t want to have to say that. I don’t want the Fed, or anyone else with power, to think that quantitative easing works, because if they think that it works, then they’re going to use it more readily in the future, which will cause yield opportunities in the economy to become more scarce and asset valuations to inflate. Financial markets will become more awkward to navigate and harder for me to earn a decent return in. I don’t want that.

I’ve had intense debates with other people on the efficacy of monetary policy, in person and online. I don’t want to have to admit that I was wrong in those debates or that my adversaries in the debates were right.

Quantitative easing is something that “works in practice, but not in theory”, which is to say that people can cite empirical cases where it seems to have helped stimulate economies that were suffering from weakness, but when you analyze what it actually entails at a fundamental level–the swapping of low-yield treasury bonds for low-yield bank deposits, two asset types that are roughly identical to each other–the theoretical basis for expecting a meaningful impact on an economy is weak. I’m a “theory” kind of person, I don’t like approaches to economics that casually bypass theory, and I don’t want those economists who have been pushing for such approaches to be rewarded with the satisfaction of having been right.

So those are my emotional biases. They aren’t really all that strong at this point, but they’re biases nonetheless. Their potential to distort my thinking is augmented by the fact that I don’t have to worry about being wrong in my views on the subject. There’s no way to know for sure whether QE3 was a meaningful benefit to the economy–there’s no reliable experiment that we can conduct to conclusively resolve the question. I’m therefore left with free rein to confidently think and say whatever I want on the topic, without fear of consequences.

Now, let’s set up a Truth Chamber on the question, to see if my deliberations and on the subject change when real consequences are held over me. We obviously need to make the claim more precise and amenable to resolution. Let’s translate “meaningful” into something like 0.25%.

Claim: “The Federal Reserve’s third quantitative easing program added an annual 0.25% (or more) to the real growth of the United States economy from its announcement in September 2012 to its September 2014 completion.”

This form of the question is more precise and easier to resolve. The way to resolve it is to literally create the counterfactual: rewind the universe back to September 2012 and let the U.S. economy grow from that point onward without QE3. If the growth rate with QE3 (which we already have data for) ends up being at least 0.25% higher the growth rate without QE3 (which we would get data for from the counterfactual), then the claim will have been shown to be true. Otherwise, it will have been shown to be false. To be fair, any outcome from this form of the experiment will likely have random variation embedded in it. To deal with that variation, we can simply run the rewind experiment a million times over: half the time with QE3, half the time without it. If the average growth rate in the trials with QE3 exceeds the average growth rate in the trials without QE3 by at least 0.25%, then the claim will have been proven to be true. And if not, then the claim will have been proven to be false.

Obviously, we can’t do this actual experiment. But we can imagine it being done–by God, or the White Queen, or whoever. Let’s imagine, then, that it is actually going to be done, and that I have been placed inside a Truth Chamber, forced to cast a secret vote on what the result will be. If I vote correctly, I will be rewarded with a plentiful supply of all of the things that I value in life. If I vote incorrectly, then I will walk away with nothing.

Which way would I vote?

When I envision myself in the scenario, the first thing that happens is that my stomach tightens. My concentration sharpens and my mind focuses in on the claim. This is no longer about ego, or reputation, or grudges, or saving face. It’s about one thing and one thing alone: getting to the truth of the matter. I need to vote correctly, period.

Upon reflection, I would still say that the claim is “false”, that the difference in growth rates with and without QE3 would not have exceeded 0.25%. But unlike before, I find myself strongly questioning that vote. The stated number, 0.25%, is not a very large number, so my margin for error is not very high. If we were to set the number at something like 1%, I would be confident in voting false, but 0.25% is small enough to make me worry about being wrong. With that said, it’s 0.25% annually over a two year period (2012 – 2014), so it’s more than just a blip.

With respect to the theory, QE may be a mere asset swap, but it has the effect of lowering long-term interest rates relative to what they would be without QE, which encourages potential homeowners and corporations to borrow. It also boosts asset prices, creating a wealth effect for the upper class that improves confidence and encourages spending. Neither of these effects was probably very large in the 2012 – 2014 period, but they still count for something. Also worth mentioning is the potential placebo effect of QE–right or wrong, many people believe QE to be efficacious, and that belief itself could have been stimulative to economic activity. Taking potential multipliers and nonlinearities into consideration, could the combined impact of these factors on the housing market, the corporate lending market, the equity market, and the general level of confidence and risk appetite in the U.S. economy have been sufficient to have added 0.25% annually in growth during the two year period? I have to admit, I’m not sure. I’m nervous to answer either way.

With respect to the empirical evidence, there have only been a handful of historical instances in which large QE programs have been implemented to stimulate weak economies. A recovery occurred in each of these instances, but it’s difficult to draw much of a conclusion from that fact, first because the sample size is very small, and second because there are an infinite number of potential confounding factors other than QE that can explain the observed result, the most important of which is the fact that weak economies tend to eventually recover on their own in time, without policymaker intervention. Still, the fact remains that in all of the historical instances that we know of in which QE was used to stimulate a weakened economy–the U.S. in the 1930s, Japan in the early naughts, and then the U.S., Europe and Japan in the current cycle–the economy eventually ended up improving. That fact has to count for something.

What the exercise reveals to me, then, is that I am not confident in rejecting the claim that QE3 had a meaningful positive impact on U.S. growth, where “meaningful” is defined to be 0.25% or more annually over the two year period. Whatever belief I might have about that claim, I need to recognize that it comes with substantial uncertainty.

Interestingly, one claim that I would be highly confident in rejecting, if I were inside a Truth Chamber, is the claim, put forward by certain fringe opponents of QE, that QE3 actually reduced growth in the US economy. That claim conflicts both with both economic theory and the available empirical evidence. If we were to run the experiment a million times over, with and without QE3, I would have no hesitation in betting against the claim that the QE3 trials would produce a lower average growth number than the non-QE3 trials. I would also be highly confident in rejecting the claim that QE, when used in the standard way to stimulate a weakened economy, creates a meaningful risk of an inflation spiral, as its opponents once warned. The actual results–in the US and elsewhere–seem to have conclusively disproven that claim.

If there is a final insight for me to glean from the exercise, then, it is probably this: Looking back at the Fed’s decision in hindsight, from the perspective of my own beliefs expressed honestly and truthfully, I would have to say that the Fed got things right when it decided to implement QE in 2012. There is a reasonable chance that the program worked to improve growth by a small but meaningful amount, and the program did not introduce any risks to price stability. Put simply, QE was a good risk-reward proposition for the Fed to take.

Summary

In summary, we human beings have the ability to think truthfully about the world, but our thinking often gets derailed by considerations that run counter to the truth. When that’s happening, it can help to stop and remember what it feels like to be in a state of mind where we are intensely focused on the truth. If we want to, we can journey into such a state of mind by envisioning ourselves entering a “Truth Chamber”, a private place where we are forced to make secret bets on our beliefs, and where our futures hinge on whether we bet correctly.

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Looking back at asset class performance over the course of market history, we notice a hierarchy of excess returns. Small caps generated excess returns over broad equities, which generated excess returns over corporate bonds, which generated excess returns over treasury bonds, which generated excess returns over treasury bills (cash), and so on. This hierarchy is illustrated in the chart and table below, which show cumulative returns and performance metrics for the above asset classes from January 1926 to March 2017 (source: Ibbotson, CRSP).

(Note: To ensure a fair and accurate comparison between equities and fixed income asset classes, we express returns and drawdowns in real, inflation-adjusted terms. We calculate volatilities and Sharpe Ratios using real absolute monthly returns, rather than nominal monthly returns over treasury bills.)

The observed hierarchy represents a puzzle for the efficient market hypothesis. If markets are efficient, why do some asset classes end up being priced to deliver such large excess returns over others? An efficient market is not supposed to allow investors to generate outsized returns by doing easy things. Yet, historically, the market allowed investors to earn an extra 4% simply by choosing equities over long-term bonds, and an extra 2% simply by choosing small caps inside the equity space. What was the rationale for that?

The usual answer given is risk. Different types of assets expose investors to different levels of risk. Risk requires compensation, which is paid in the form of a higher return. The additional 4% that equity investors earned over bond investors did not come free, but represented payment for the increased risk that equity investing entails. Likewise, the 2% bonus that small cap investors earned over the broad market was compensation for the greater risk associated with small companies.

A better answer, in my view, is that investors didn’t know the future. They didn’t know that equity earnings and dividends were going to grow at the pace that they did. They didn’t know that small cap earnings and dividends were going to grow at an even faster pace. They didn’t know that inflation was going to have the detrimental long-term effects on real bond returns that it had. And so on. Amid this lack of future knowledge, they ended up pricing equities to outperform bonds by 4%, and small caps to outperform the broad market by 2%. Will we see a similar outcome going forward? Maybe. But probably not.

Let’s put aside the question of whether differences in “risk”, whatever that term is used to mean, can actually justify the differences in excess returns seen in the above table. In what follows, I’m going to argue that if they can, then as markets develop and adapt over time, those excess returns should fall. Risk assets should become more expensive, and the cost of capital paid by risk issuers should come down.

The argument is admittedly trivial. I’m effectively saying that improvements in the way a market functions should lead to reductions in the costs that those who use it–those who seek capital–should have to pay. Who would disagree? Sustainable reduction in issuer cost is precisely what “progress” in a market is taken to mean. Unfortunately, when we flip the point around, and say that the universe of risk assets should grow more expensive in response to improvements, people get concerned, even though the exact same thing is being said.

To be clear, the argument is normative, not descriptive. It’s an argument about what should happen, given a certain assumption about the justification for excess returns. It’s not an argument about what actually has happened, or about what actually will happen. As a factual matter, on average, the universe of risk assets has become more expensive over time, and implied future returns have come down. The considerations to be discussed in this piece may or may not be responsible for that change.

We tend to use the word “risk” loosely. It needs a precise definition. In the current context, let “risk” refer to any exposure to an unattractive or unwanted possibility. To the extent that such an exposure can be avoided, it warrants compensation. Rational investors will demand compensation for it. That compensation will typically come in the form of a return–specifically, an excess return over alternatives that successfully avoid it, i.e., “risk-free” alternatives.

We can arbitrarily separate asset risk into three different types: price risk, inflation risk, and fundamental risk.

The proper way to answer the question is to identify all of the differences between the government bond and the cash, and to then settle on a rate of return (and therefore a price) that fairly compensates for them, in total.

The primary difference between the government bond and the cash is that the cash is liquid. You can use it to buy things, or to take advantage of better investment opportunities that might emerge. Of course, you can do the same with the government bond, but you can’t do it directly. You have to sell the bond to someone else. What will its price in the market be? How will its price behave over time? You don’t know. When you go to actually sell it, the price could end up being lower than the price you paid for it, in which case accessing your money will require you to accept a loss. We call exposure to that possibility price risk. The bond contains it, cash does not. To compensate, the bond should offer an excess return over cash, which is the “price-risk-free” alternative.

To fully dismiss the price risk in a government bond investment, you would have to assume total illiquidity in it. Total illiquidity is an extreme cost that dramatically increases the excess return necessary to draw an investor in. That said, price risk is a threat to more than just your liquidity. It’s a threat to your peace of mind, to your measured performance as an investor or manager, and to your ability to remain in leveraged trades. And so even if you have no reason to want liquid access to your money, no reason to care about illiquidity, the risk that the price of an investment might fall will still warrants some compensation.

A second category of risk is inflation risk. Inflation risk is exposure to the possibility that the rate of inflation might unexpectedly increase, reducing the real value of a security’s future payouts. The cash is offering payouts tied to the short-term rate, which (typically) gets adjusted in response to changes in inflation. It therefore carries a measure of protection from that risk. The bond, in contrast, is offering a fixed payout 10 years from now, and is fully exposed to the risk. To compensate for the difference, the bond should offer an excess return over cash.

Returning to the scenario, let’s assume that you assess all of the differences between the bond and cash, to include the bond’s price risk and inflation risk, and conclude that a 2% excess return in the bond is warranted. Your estimate of fair value, then, will be $67.55, which equates to a 4% yield-to-maturity (YTM).

Fundamental Risk: An Introduction to Lotto Shares

A security is a stream of cash flows and payouts. Fundamental risk is risk to those cash flows and payouts–the possibility that they might not pay out. We can illustrate its impact with an example.

In the previous scenario, you estimated fair value for the government bond to be $67.55, 4% YTM. Let’s assume that you’re now forced to invest your entire net worth into either that bond at that price, or into a new type of security that’s been introduced into the market, a “Lotto Share.”

Lotto Share: A government bond with a random payout. Lotto Shares are issued in separate share classes. At the maturity date of each share class, the government flips a fair coin. If the coin ends up heads (50% chance), the government exchanges each outstanding share in the share class for a payment of $200. If the coin ends up tails (50% chance), the government makes no exchange, and each outstanding share in the share class expires worthless.

Before you make your choice, note that the Lotto Shares being offered all come from the same class, Class “A.” All of their payouts will therefore be decided by the same single coin flip, to take place at maturity 10 years from now.

The question: What is fair value for a Lotto Share?

To answer the question, try to imagine that you’re actually in the scenario, forced to choose between the two options. What price would Lotto Shares have to sell at in order for you to choose to invest in them? Would $67.55 be appropriate? How about $50? $25? $10? $5? $1? One penny? Is there any price that would interest you?

It goes without saying that your answer will depend on whether you can diversify among the two options. Having the entirety of your portfolio, or even a sizeable portion thereof, invested in a security that has a 50% chance of becoming worthless represents an enormous risk. You would need the prospect of an enormous potential reward in order to take it–if you were willing to take it at all. But if you have the option to invest much smaller portions of your portfolio into the security, if not simply for the “fun” of doing so, the potential reward won’t need to be as large.

Assume that you do have the ability to diversify between the two options. The question will then take on a second dimension: allocation. At each potential price for Lotto Shares, ranging from zero to infinity, how much of your portfolio would you choose to allocate to them?

Let’s assume that Lotto Shares are selling for the same price as normal government bonds, $67.55. How much of your portfolio would you choose to put into them? If you’re like most investors, your answer will be 0%, i.e., nothing. To understand why, notice that Lotto Shares have the same expected (average) payout as normal government bonds, $100 ($200 * 50% + $0 * 50% = $100). The difference is that they pay that amount with double-or-nothing risk–at maturity, you’re either going to receive $200 or $0. That risk requires compensation–an excess return–over the risk-free alternative. Lotto Shares priced identically to normal government bonds (the risk-free alternative) do not offer such compensation, therefore you’re not going to want to allocate anything to them. You’ll put everything in the normal government bond.

Now, in theory, we can envision specific situations where you might actually want double-or-nothing risk. For example, you might need lifesaving medical treatment, and only have half the money needed to cover the cost. In that case, you’ll be willing to make the bet even without compensation–just flip the damn coin. If it comes back heads, you’ll survive, if it comes back tails… who cares, you would have died anyways. Alternatively, you might be managing other people’s money under a perverse “heads-you-win, tails-they-lose” incentive arrangement. In that case, you might be perfectly comfortable submitting the outcome to a coin flip, without receiving any extra compensation for the risk–it’s not a risk to you. But in any normal, healthy investment situation, that’s not going to be the case. Risk will be unwelcome, and you won’t willingly take it on unless you get paid to do so.

Note that the same point holds for price risk and inflation risk. Prices can go up in addition to down, and inflation can go down in addition to up. You can get lucky and end up benefitting from having taken those risks. But you’re not a gambler. You’re not going to take them unless you get compensated.

The price and allocation question, then, comes down to a question of compensation: at each level of potential portfolio exposure, what expected (or average) excess return over the risk-free alternative (i.e., normal government bonds) is necessary to compensate for the double-or-nothing risk inherent in Lotto Shares? The following table lists the expected 10 year annualized excess returns for Lotto Share at different prices. Note that these are expected returns. They’re only going to hold on average–in actual practice, you’re going to get double-or-nothing, because the outcome is going to be submitted to only one flip.

We can pose the price and allocation question in two different directions:

(1) (Allocation –> Price): Starting with an assumed allocation–say, 40%–we could ask: what price and excess return for Lotto Shares would be needed to get you to allocate that amount, i.e., risk that amount in a coin flip?

(2) (Price –> Allocation): Starting with an assumed price–say, $25, an annual excess return of 10.87%–we could ask: how much of your portfolio would you choose to allocate to Lotto Shares, if offered that price?

Up to now, we’ve focused only on fundamental risk, i.e., risk to a security’s cash payouts. In a real world situation, we’ll need to consider price risk. As discussed earlier, price risk requires compensation in the form of an excess return over the “price-risk-free” alternative, cash. But notice that in our scenario, we don’t have the option of holding cash. Our options are to invest in Lotto Shares or to invest in normal government bonds. The factor that requires compensation, then, is the difference in price risk between these two options.

Because Lotto Shares carry fundamental risk, their price risk will be greater than the price risk of normal government bonds. As a general rule, fundamental risk creates its own price risk, because it forces investors to grapple with the murky question of how that risk should be priced, along with the even murkier question of how others in the market will think it should be priced (in the Keynesian beauty contest sense). Additionally, as normal government bonds approach maturity, their prices will become more stable, converging on the final payment amount, $100. As Lotto Shares approach maturity, the opposite will happen–their prices will become more volatile, as more and more investors vacillate on whether to stay in or get out in advance of the do-or-die coin flip.

That said, price risk is not the primary focus here. To make it go away as a consideration, let’s assume that once we make our initial purchases in the scenario, the market will close permanently, leaving us without any liquidity in either investment. We’ll have to hold until maturity. That would obviously be a disadvantage relative to a situation where we had liquidity and could sell, but the disadvantage applies equally to both options, and therefore cancels out of the pricing analysis.

Returning to the question of Lotto Share pricing, for any potential investor in the market, we could build a mapping between each possible price for a Lotto Share, and the investor’s preferred allocation at that price. Presumably, at all prices greater than $67.55 (the price of the normal government bond), the investor’s preferred allocation will be 0%. As the price is reduced below that price, the preferred allocation will increase, until it hits a ceiling representing the maximum percentage of the portfolio that the investor would be willing to risk in a coin flip, regardless of how high the potential payout might be. The mappings will obviously be different for different investors, determined by their psychological makeups and the specific financial and life circumstances they are in.

I sat down and worked out my own price-allocation mapping, and came up with the table shown below. The first column is the Lotto Share price. The second column is my preferred allocation at that price. The third and fourth column are the absolute dollar amounts of the excess gains (on heads) and excess losses (on tails) that would be received or incurred if a hypothetical $1,000,000 portfolio were allocated at that percentage:

Working through the table, if I were managing my own $1,000,000 portfolio, and I were offered a Lotto Share price of $65, I would be willing to invest 1%, which would entail risking $14,800 in a coin flip to make $25,969 on heads. If I were offered a price of $40, I would be willing to invest 5%, which would entail risking $74,000 in a coin flip to make $226,000 on heads. If I were offered $15, I would be willing to invest 20%, which would entail risking $296,000 in a coin flip to make $2,750,667 on heads. And so on.

Interestingly, I found myself unwilling to go past 20%. To put any larger amount at risk, I would need the win-lose odds to be skewed in my favor. In Lotto Shares, they aren’t–they’re even 50/50. What’s skewed in my favor is the payout if I happen to win–that’s very different.

The example illustrates the extreme impact that risk-aversion has on asset valuation and asset allocation. To use myself as an example, you could offer me a bargain basement price of $5 for a Lotto Share, corresponding to a whopping 35% expected annual return over 10 years, and yet if that expected return came with double-or-nothing risk attached, I wouldn’t be willing to allocate anything more than a fifth of my assets to it.

Interestingly, when risk is extremely high, as it is with Lotto Shares, the level of interest rates essentially becomes irrelevant. Suppose that you wanted to get me to allocate more than 20% of my portfolio to Lotto Shares. To push me to invest more, you could drop the interest rate on the government bond to 2%, 0%, -2%, -4%, -6%, and so on–i.e., try to “squeeze” me into the Lotto Share, by making the alternative look shitty. But if I’m grappling with the possibility of a 50% loss possibility on a large portion of my portfolio, your tiny interest rate reductions will make no difference at all to me. They’re an afterthought. That’s why aggressive monetary policy is typically ineffective at stimulating investment during downturns. To the extent that investors perceive investments to be highly risky, they will require huge potential rewards to get involved. Relative to those huge rewards, paltry shifts in the cost of borrowing or in the interest rate paid for doing nothing will barely move the needle.

I would encourage you to look at the table and try to figure out how much you would be willing to risk at each of the different prices. If you’re like me, as you grapple with the choice, you will find yourself struggling to find a way to get a better edge on the flip, or to somehow diversify the bet. Unfortunately, given the constraints of the scenario, there’s no way to do either.

Interestingly, if the price-allocation mapping of all other investors in the market looked exactly like mine, Class “A” Lotto Shares would never be able to exceed 20% of the total capitalization of the market. No matter how much it lowered the price, the government would not be able to issue any more of them beyond that capitalization, because investors wouldn’t have any room in their portfolios for the additional risk.

Adding New Lotto Share Classes to the Market

Let’s examine what happens to our estimate of the fair value of Lotto Shares when we add new share classes to the market.

Assume that three new share classes are added, so that the we now have four –“A”, “B”, “C”, “D”. Each share class matures in 10 years, and pays out $200 or $0 based on the result of a single coin flip. However, and this is crucial, each share class pays out based on its own separate coin flip. The fundamental risk in each share class is therefore idiosyncratic–independent of the risks in the other share classes.

To summarize, then, you have to invest your net worth across the following options:

Whatever our fair value estimate happens to be, it should be the same for all Lotto Shares in the market, given that those shares are identical in all relevant respects. Granted, if the market supplies of the different share classes end up being different, then they might end up trading at different prices, similar to the way different share classes of preferred stocks sometimes trade at different prices. But, as individual securities, they’ll still be worth the same, fundamentally.

Obviously, if you choose to allocate to Lotto Shares in this new scenario, you’re going to want to diversify your exposure equally across the different share classes. That will make the payout profile of the investment more attractive. Before, you only had one share class to invest in–Class “A”. The payout profile of that investment was a 50% chance of $200 (heads) and a 50% chance of $0 (tails). If you add a new share class to the mix, so that you have an equal quantity of two in the portfolio, your payout will be determined by two coin flips instead of one–a coin flip that decides your “A” shares and a coin flip that decides your “B” shares. On a per share basis, the payout profile will then be a 25% chance of receiving $200 (heads for “A”, heads for “B”), a 50% chance of receiving $100 (heads for “A”, tails for “B” or tails for “B”, heads for “A”), and a 25% chance of receiving $0 (tails for “A”, tails for “B”). If you add two more shares classes to the mix, so that you have an equal quantity of four in the portfolio, the payout profile will improve even further, as shown in the table below.

In the previous scenario, the question was, what excess return over normal government bonds would Lotto Shares need to offer in order to get you to invest in them, given that the investment has a 50% chance of paying out $200 and a 50% chance of paying out $0? With four share classes in the mix, the question is the same, except that the investment, on a per share basis, now has a 6.25% chance of paying out $0, a 25% chance of paying out $50, a 37.5% chance of paying out $100, a 25% chance of paying out $150, and a 6.25% chance of paying out $200. As before, the expected payout is $100 per share. The difference is that this expected payout comes with substantially reduced risk. Your risk of losing everything in it, for example, is longer 50%. It’s 6.25%, a far more tolerable number.

Obviously, given the significant reduction in the risk, you’re going to be willing to accept a much lower excess return in the shares to invest in them, and therefore you’ll be willing to pay a much higher price. In a way, this is a very surprising conclusion. It suggests that the estimated fair value of a security in a market can increase simply by the addition of other, independent securities into the market. If you have an efficient mechanism through which to diversify across those securities, you won’t need to take on the same risk in owning each individual one. But that risk was precisely the basis for there being a price discount and an excess return in the shares–as it goes away, the discount and excess return can go away.

In the charts below, we show the payout profiles for Lotto Share investments spread equally across 100, 1,000, and 10,000 different Lotto Share Classes. As you can see, the distribution converges ever more tightly around the expected (average) $100 payout per share.

As you can see from looking at this last chart, if you can invest across 10,000 independent Lotto Shares, you can effectively turn your Lotto Share investment into a normal government bond investment–a risk-free payout. In terms of the probabilities, the cumulative total payout of all the shares (which will be determined by the number of successful “heads” that come up in 10,000 flips), divided by the total number of shares, will almost always end up equaling a value close to $100, with only a very tiny probabilistic deviation around that number. In an extreme case, the aggregate payout may end up being $98 per share or $102 per share–but the probability that it will be any number outside that is effectively zero. And so there won’t be any reason for Lotto Shares to trade at any discount relative to normal government bonds. The excess returns that had to be priced into them in earlier scenarios where their risks couldn’t be pooled together will be able to disappear.

Equities as Lotto Shares

Dr. Hendrik Bessembinder of Arizona State University recently published a fascinating study in which he examined the return profiles of individual equity securities across market history. He found that the performance is highly positively skewed. Most individual stocks perform poorly, while a small number perform exceptionally well. The skew is vividly illustrated in the chart below, which shows the returns of 54,015 non-overlapping samples of 10 year holding periods for individual stocks:

The majority of stocks in the sample underperformed cash. Almost half suffered negative returns. A surprisingly large percentage went all the way down to zero. The only reason the market as a whole performed well was because a small number of “superstocks” generated outsized returns. Without the contributions of those stocks, average returns would have been poor, well below the returns on fixed income of a similar duration. To say that individual stocks are “risky”, then, is an understatement. They’re enormously risky.

As you can probably tell, our purpose in introducing the Lotto Shares is to use them to approximate the large risk seen in individual equity securities. The not-so-new insight is that by combining large numbers of them together into a single equity investment, we can greatly reduce the aggregate risk of that investment, and therefore greatly reduce the excess return needed to compensate for it.

This is effectively what we’re doing when we go back into the data and build indices in hindsight. We’re taking the chaotic payout streams of individual securities in the market (the majority of which underperformed cash) and merging them together to form payout streams that are much smoother and well-behaved. In doing so, we’re creating aggregate structures that carry much lower risk than the actual individual securities that the actual investors at the time were trading. The fact that it may have been reasonable for those investor to demand high excess returns over risk-free alternatives when they were trading the securities does not mean that it would be similarly reasonable for an investor today, who has the luxury of dramatically improved market infrastructure through which to diversify, to demand those same excess returns.

When we say that stocks should be priced to deliver large excess returns over long-term bonds because they entail much larger risks, we need to be careful not to equivocate on that term, “risk”. The payouts of any individual stock may carry large risks, but the payouts of the aggregate universe of stocks do not. As the chart below shows, the aggregate equity payout is a stream of smooth, reasonably well-behaved cash flows, especially when the calamity of the Great Depression (a likely one-off historical event) is bracketed out.

(Note: We express the dividend stream on a real total return basis, assuming each dividend is reinvested back into the equity at market).

In terms of stability and reliability, that stream is capable of faring quite well in a head-to-head comparison with the historical real payout stream of long-term bonds. Why then, should it be discounted relative to bonds at such a high annual rate, 4%?

A similar point applies to the so-called “small cap” risk premium. As Bessembinder’s research confirms, individual small company performance is especially skewed. The strict odds of any individual small company underperforming, or going all the way to zero, is very high–much higher than for large companies. Considered as isolated individual investments, then, small companies merit a substantial price discount, a substantial excess return, over large companies. But when their risks are pooled together, the total risk of the aggregate goes down. To the extent that investors have the ability to efficiently invest in that aggregate, the required excess return should come down as well.

The following chart shows the historical dividend stream (real total return basis) of the smallest 30% of companies in the market alongside that of the S&P 500 from January 1928 to March 2017:

Obviously, pooling the risks of individual small caps together doesn’t fully eliminate the risk in their payouts–they share a common cyclical risk, reflected in the volatility of the aggregate stream. If we focus specifically on the enormous gash that took place around the Great Depression, we might conclude that a 2% discount relative to large caps is appropriate. But when we bracket that event out, 2% starts to look excessive.

Progress in Diversification: Implications for the Cost of Capital

In the earlier scenarios, I told you up front that each class of Lotto Shares has a 50% chance of paying out $200. In an actual market, you’re not going to get that information so easily. You’re going to have to acquire it yourself, by doing due diligence on the individual risk asset you’re buying. That work will translate into time and money, which will subtract from your return.

To illustrate, suppose that there are 10,000 Lotto Share Classes in the market: “A”, “B”, “C”, “D”, “E”, etc. Each share class pays out P(A), P(B), P(C), P(D), P(E), etc., with independent probabilities Pr(A), Pr(B), Pr(C), Pr(D), Pr(E), etc. Your ability to profitably make an investment that diversifies among the different share classes is going to be constrained by your ability to efficiently determine what all of those numbers are. If you don’t know what they are, you won’t have a way to know what price to pay for the shares–individually, or in a package.

Assume that it costs 1% of your portfolio to determine each P and Pr for an individual share class. Your effort to put together a well-diversified investment in Lotto Shares, an investment whose payout mimics the stability of the normal government bond’s payout, will end up carrying a large expense. You will either have to pay that expense, or accept a poorly diversified portfolio, with the increased risk. Both disadvantages can be fully avoided in a government bond, and therefore to be willing to invest in the Lotto Share, you’re going to need to be compensated. As always, the compensation will have to come in the form of a lower Lotto Share price, and a higher return.

Now, suppose that the market develops mechanisms that allows you to pool the costs of building a diversified Lotto Share portfolio together with other investors. The cost to you of making a well-diversified investment will come down. You’ll therefore be willing to invest in Lotto Shares at higher prices.

Even better, suppose that the investment community discovers that it can use passive indexing strategies to free-load on the fundamental Lotto Share work that a small number of active investors in the market are doing. To determine the right price to pay, people come to realize that they can drop all of the fretting over P, Pr, and so on, and just invest across the whole space, paying whatever the market is asking for each share–and that they won’t “miss” anything in terms of returns. The cost of diversification will come down even further, providing a basis for Lotto Share prices to go even higher, potentially all the way up to the price of a normal government bond, a price corresponding to an excess return of 0%.

The takeaway, then, is that as the market builds and popularizes increasingly cost-effective mechanisms and methodologies for diversifying away the idiosyncratic risks in risky investments, the price discounts and excess returns that those investments need to offer, in order to compensate for the costs and risks, comes down. Very few would dispute this point in other economic contexts. Most would agree, for example, that the development of efficient methods of securitizing mortgage lending reduces the cost to lenders of diversifying and therefore provides a basis for reduced borrowing costs for homeowners–that’s its purpose. But when one tries to make the same argument in the context of stocks–that the development of efficient methods to “securitize” them provides a basis for their valuations to increase–people object.

In the year 1950, the average front load on a mutual fund was 8%, with another 1%annual advisory fee added in. Today, given the option of easy indexing, investors can get convenient, well-diversified exposure to many more stocks than would have been in a mutual fund in 1950, all for 0%. This significant reduction in the cost of diversification warrants a reduction in the excess return that stocks are priced to deliver, particularly over safe assets like government securities that don’t need to be diversified. Let’s suppose with all factors included, the elimination of historical diversification costs ends up being worth 2% per year in annual return. Parity would then suggest that stocks should offer a 2% excess return over government bonds, not the historical 4%. Their valuations would have a basis to rise accordingly.

Now, to clarify. My argument here is that the ability to broadly diversify equity exposure in a cost-effective manner reduces the excess return that equities need to offer in order to be competitive with safer asset classes. In markets where such diversification is a ready option–for example, through low-cost indexing–valuations deserve to go higher. But that doesn’t mean that they actually will go higher. Whether they actually will go higher is not determined by what “deserves” to happen, but by what buyers and sellers actually choose to do, what prices they agree to transact at. They can agree to transact at whatever prices they want.

The question of whether the increased availability and popularity of equity securitization has caused equity valuations to go higher is an interesting question. In my view, it clearly has. I would offer the following chart as circumstantial evidence.

Notice the large, sustained valuation jump that took place in the middle of the 1990s. Right alongside it, there was a large, sustained jump in the percentage of the equity market invested through mutual funds and ETFs. Correlation is not causation, but there are compelling reasons to expect a relationship in this case. Increased availability and popularity of vehicles that allow for cheap, convenient, well-diversified market exposure increases the pool of money inclined to bid on equities as an asset class–not only during the good times, but also when buying opportunities arise. It’s reasonable to expect that the result would be upward pressure on average valuations across the cycle, which is exactly what we’ve seen.

History: The Impact of Learning and Adaptation

One problem with using Lotto Shares as an analogy to risk assets, equities in particular, is that Lotto Shares have a definite payout P and a definite probability Pr that can be known and modeled. Risk assets don’t have that–the probabilities around their payouts are themselves uncertain, subject to unknown possibility. That uncertainty is risk–in the case of equities, it’s a substantial risk.

If we’re starting out from scratch in an economy, and looking out into the future, how can we possibly know what’s likely to happen to any individual company, or to the corporate sector as a whole? How can we even guess what those probabilities are?

But as time passes, a more reliable recorded history will develop, a set of known experiences to consult. As investors, we’ll be able to use that history and those experiences to better assess what the probabilities are, looking out into the future. The uncertainty will come down–and with it the excess return needed to justify the risks that we’re taking on.

We say that stocks should be expensive because interest rates are low and are probably going to stay low forever. The rejoinder is: “Well, they were low in the 1940s and 1950s, yet stocks weren’t expensive.” OK, but so what? Why does that matter? All it means is that, in hindsight, investors in the 1940s and 1950s got valuations wrong. Should we be surprised?

Put yourself in the shoes of an investor in that period, trying to determine what the future for equities might look like. You have the option of buying a certain type of security, a “stock”, that pays out company profits. In the aggregate, do you have a way to know what the likely growth rates of those profits will be over time? No. You don’t have data. You don’t have a convenient history to look at. Consequently, you’re not going to be able to think about the equity universe in that way. You’re going to have to stay grounded at the individual security level, where the future picture is going to be even murkier.

In terms of price risk, this is what the history of prices will look like from your vantage point:

Judging from the chart, can you reliably assess the risk of a large upcoming drop? Can you say, with any confidence, that if a drop like the one that happened 20 odd years ago happens again, that it will be recovered in due course? Sure, you might be able to take solace in the fact that the dividend yield, at 5.5%, is high. But high according to who? High relative to what? The yield isn’t high relative to what it was just a few years ago, or to what it was after the bubble burst. One can easily envision cautious investors pointing that out to you. Something like this, taken right out of that era:

Now, fast forward to the present day. In terms of estimating future growth rates and returns on investment, you have the chart below, a stream of payouts that, on a reinvested basis, has grown at a 6% average real rate over time, through the challenges of numerous economic cycles, each of which was different in its own way. Typical investors may not know the precise number, but they’re aware of the broader historical insight, which is that equities offer the strongest long-term growth potential of any asset class, that they’re where investors should want to be over the long haul: “Stocks For The Long Run.” That insight has become ingrained in the financial culture. One can say that its prevalence is just another symptom of the “bubble” that we’re currently in, but one has to admit that there’s at least some basis for it.

Now, I’ll be the first to acknowledge that the 6% number is likely to be lower going forward. In fact, that’s the whole point–equity returns need to be lower, to get in line with the rest of the asset universe. The mechanism for the lower returns, in my view, is not going to be some kind of sustained mean-reversion to old-school valuations, as the more bearishly inclined would predict. Rather, it’s going to come directly from the market’s expensiveness itself, from the fact that dividend reinvestments, buybacks and acquisitions will all be taking place at much higher prices than they did in the past. On the assumption that current valuations hold, I estimate that long-term future returns will be no more than 4% real. To get that number, I recalculate the market’s historical prices based on what they would have been if the market had always traded at its current valuation–a CAPE range of 25 to 30. With the dividends reinvested at those higher prices, I then calculate what the historical returns would have been. The answer: 4% real, reflecting the impact of the more expensive reinvestment, which leads to fewer new shares purchased, less compounding, and a lower long-term return. Given the prices current investors are paying, they have little historical basis for expecting to earn any more than that. If anything, they should expect less. The return-depressing effect of the market’s present expensiveness is likely to be amplified by the fact that there’s more capital recycling taking place today–more buybacks, acquisitions, etc., all at expensive prices–and less growth-producing real investment. So 4% represents a likely ceiling on returns, not a floor.

Regardless of the specific return estimate that we settle on, the point is, today, the facts can be known, and therefore things like this can be realistically modeled–not with anything close to certainty, but still in a way that’s useful to constrain the possibilities. Investors can look at a long history of US equity performance, and now also at the history of performance in other countries, and develop a picture of what’s likely to happen going forward. In the distant past, investors did not have that option. They had to fly blind, roll the dice on this thing called the “market.”

In terms of price risk, this is what your rear view mirror looks like today:

Sure, you might get caught in a panic and lose a lot of money. But history suggests that if you stick to the process, you’ll get it back in due course. That’s a basis for confidence. Importantly, other investors are aware of the same history that you’re aware of, they’ve been exposed to the same lessons–“think long-term”, “don’t sell in a panic”, “stocks for the long run.” They therefore have the same basis for confidence that you have. The result is a network of confidence that further bolsters the price. Panics are less likely to be seen as reasons to panic, and more likely to be seen as opportunities to be taken advantage of. Obviously, panics will still occur, as they must, but there’s a basis for them to be less chaotic, less extreme, less destructive than they were in market antiquity.

Most of the historical risk observed in U.S. equities is concentrated around a single event–the Great Depression. In the throes of that event, policymakers faced their own uncertainties–they didn’t have a history or any experience that they could consult in trying to figure out how to deal with the growing economic crisis. But now they do, which makes it extremely unlikely that another Great Depression will ever be seen. We saw the improved resilience of the system in the 2008 recession, an event that had all of the necessary ingredients to turn itself into a new Great Depression. It didn’t–the final damage wasn’t even close to being comparable. Here we are today, doing fine.

An additional (controversial) factor that reduces price risk relative to the past is the increased willingness of policymakers to intervene on behalf of markets. Given the lessons of history, policymakers now have a greater appreciation for the impact that market dislocations can have on an economy. Consequently, they’re more willing to actively step in to prevent dislocations from happening, or at least craft their policy decisions and their communications so as to avoid causing dislocations. That was not the case in prior eras. The attitude towards intervention was moralistic rather than pragmatic. The mentality was that even if intervention might help, it shouldn’t happen–it’s unfair, immoral, a violation of the rules of the game, an insult to the country’s capitalist ethos. Let the system fail, let it clear, let the speculators face their punishments, economic consequences be damned.

To summarize: over time, markets have developed an improved understanding of the nature of long-term equity returns. They’ve evolved increasingly efficient mechanisms and methodologies through which to manage the inherent risks in equities. These improvements provide a basis for average equity valuations to increase, which is something that has clearly been happening.

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The current market environment is made difficult by the fact that investors have nowhere that they can go to confidently earn a decent return. There are no good deals to be found anywhere, in any area of the investment universe. Some see that as a failure of markets, but I see it as an achievement. A market that is functioning properly should not offer investors good deals. When adjusted for risk, every deal that’s on the table should be just as good as every other. If any deal shows itself to be any better than any other, market participants should notice it and quickly take it off the table.

We live in a world in which there is a large demand for savings, but a small relative supply of profitable new investment opportunities to deploy those savings into. We can debate the potential causes of this imbalance–aging demographics, falling population growth, stagnation in innovation, zero-sum substitution of technology for labor, globalization, rising wealth inequality, excessive debt accumulation, and so on. But the effect is clear: central banks have to set interest rates at low levels in order to stimulate investment, encourage consumption, and maintain sufficient inflationary pressure in the economy. The tool they use may not work very well, but it’s the only tool they have.

Low interest rates, of course, mean low returns for whoever decides to hold the economy’s short-term money. In a properly functioning market, those low returns should not stay contained to themselves. They should propagate out and infect the rest of the investment universe. And that’s exactly what we’ve seen them do. As it’s become clear that historically low interest rates are likely to persist long out into the future–and quite possibly forever–every item on the investment menu has become historically expensive.

Thinking concretely, what types of things can a value-conscious investor do to cope with the current environment? Personally, I can only think of two things: (1) Figure out a way to time the market, or (2) Try to find places inside the market where value still exists. With respect to the first, market timing, I already shared my best idea, which is to go to cash when both the price trend and the trend in economic fundamentals are negative, and to be long equities in all other circumstances–regardless of valuation. That approach continues to work–it’s still long the market, and hasn’t fallen prey to any of the usual fake-outs (fears of recession, concerns about valuation, etc.). With respect to the second, finding value inside the market, I think I know of a good place. That’s what this piece is going to be about.

The specific part of the market that I’m going to look at is the space of preferred stocks, a space riddled with inefficiencies. There are two individual securities in that space that I consider to be attractive values: two large bank convertible preferred issues. At current prices, they both yield around 6.15%. They carry very little credit risk, they can’t be called in, and their dividends are tax-advantaged. The fact that they could be priced so attractively in a market filled with so much mediocrity is proof that markets are not always efficient.

I should say at the outset that I don’t have a strong view on the near-term direction of long-term interest rates. My bias would be to bet against the consensus that they’re set to rise appreciably from here, but I can’t make that bet with any confidence. If they do rise appreciably, the securities that I’m going to mention will perform poorly, along with pretty much everything else in the long-term fixed income space. So if that’s your base case, don’t interpret my sharing them as any kind of recommendation to buy. Treat them instead as ideas to put on a fixed income shopping list, to consult when the time is right.

The piece has five sections (click on the hyperlinks below to fast-forward to any of them):

In the first section, I explain how preferred stocks work. (Highlight: A helpful “simultaneous trade” analogy that investors can use in thinking about and evaluating the impact of callability.)

In the second section, I analyze the valuation of preferred stocks as a group, comparing their present and historical yields to the yields on high yield corporate, investment grade corporate, emerging market USD debt, and treasury debt. I also quantify the value of the embedded tax-advantage they offer. (Highlight: Tables and charts comparing yields and spreads on different fixed income sectors. Periods examined include 1997 to 2017 and 1910 to 1964.)

In the third section, I discuss the unique advantages that financial preferred stocks offer in the current environment. (Highlight: A chart of the Tangible Common Equity Ratios of the big four US banks, showing just how strong their balance sheets are at present.)

In the fourth section, I introduce the two preferred stocks and examine the finer details of their structures. (Highlight: A price chart and a table that simplifies all of the relevant information)

In the fifth section, I make the case for why the two preferred stocks are attractive values. I also offer possible reasons why the market has failed to value them correctly, looking specifically at issues associated with duration, supply, and index exclusion. (Highlight: I look at one of the most expensive fixed income securities in the entire US market–a 1962 preferred issue of a major railroad company that still trades to this day. I discuss how supply-related distortions have helped pushed it to its currently absurd valuation.)

Preferred Stocks: A Primer

Recall that a common stock is a claim on the excess profits of a corporation, which are ultimately paid out as dividends over time. A common stock is also a claim of control over the company’s activities, expressed through voting rights. A preferred stock, in contrast, is a claim to receive fixed periodic dividend payments on the initial amount of money delivered to the company in the preferred investment–the “par” value of each preferred share. Such a claim typically comes without any voting rights, but voting rights can sometimes be triggered if the promised payments aren’t made. In a liquidation, preferred stock is senior to common stock, but subordinate to all forms of debt.

Importantly, a preferred stock’s claim to dividends is contingent upon the company actually being able to make the promised payments. If the company can’t make those payments, it won’t go into default like it would for a missed bond payment. Rather, it will simply be prohibited from paying out dividends to its common shareholders, and also from repurchasing any of its common shares. This constraint is what makes preferred shares worth something as pieces of paper. If a company fails to fulfill its obligations to its preferred shareholders, its common shareholders will have no prospect of earning cash flows on their investments, and therefore their shares–their pieces of paper–won’t carry value.

A preferred share can be cumulative or non-cumulative. When a preferred share is cumulative, any past missed dividend payments, going all the way back to the share’s date of issuance, have to be paid in full before any common dividends can be paid or any common shares bought back. When a preferred share is non-cumulative, this restraint is narrowed to a given period of time, usually a calendar quarter. The company cannot pay dividends in a given calendar quarter or buy back shares in that quarter unless all preferred dividends owed for that quarter have been paid.

Preferred shares usually come with a call feature that allows the company to buy them back at par after some specified date. The best way to conceptualize the impact of this feature is to think of a callable preferred share as representing two separate investment positions. First, the preferred share itself, a perpetual security that pays out some fixed yield. Second, a call option that is simultaneously sold on those shares. When you buy a callable preferred, you’re effectively putting yourself into both types of trades–you’re purchasing a perpetual fixed income security, and you’re simultaneously selling a call option against it at a strike price of par, exerciseable after some specified date.

The existence of a call option on a preferred share significantly complicates its valuation. For an illustration, let’s compare the case of a non-callable share with the case of a callable one. In the first case, suppose that a company issues a non-callable 4% preferred share to an investor at a par value of $25. Shortly after issuance, yields on similar securities fall from 4% to 3%. The share has to compete with those securities, and so its price should rise to whatever price offers a 3% yield, matching theirs. In the current case, that price would be $33 (logic: $1 / $33 = 3%). But now suppose that the share comes with a call option that allows the company to redeem it at par, $25, in five years. With the impact of the call option added in, a price of $33 will no longer makes sense. If an investor were to buy at that price, and the security were to eventually be called in at par, $25, she would lose $8 per share on the call ($33 – $25 = $8). Instead of being 3%, her total return would end up being negative.

For any assumed purchase price, then, the investor has to incorporate the call–both its impact on the total return if exercised, and its likelihood of being exercised–into the estimate of the total return. In the above scenario, if we assume that the call option becomes exerciseable 5 years from now, and that it will, in fact, be exercised, then the right price for the shares, the price that implies a 3% yield competitive with the rest of the market, is not $33, but rather $26.16. At that purchase price, the $5 of dividends that will be collected over the 5 years until the call date, minus the $1.16 that will be lost from the purchase price when the shares are called in at $25, will produce a final total return that annualizes to 3%, equal to the prevailing market rate.

Now, for some definitions. The “current yield” of a security is its annual dividend divided by its market price. The “yield-to-call” of a callable security is the total return that it will produce on the assumption that the investor holds it until the call date, at which point it gets called in. The “yield-to-worst” of a callable security is the lesser of its current yield and its yield-to-call. This yield is referred to as a yield to “worst” because it represents the worst case total return that an investor can expect to earn if she holds to maturity–assuming, of course, that the shares pay out as promised.

Companies typically decide whether or not to call in preferred shares based on whether they can get better rates in the market by issuing out new ones (and the new issuance need not be preferred–it could be debt or even other forms of equity, if the cost to the company is less). For that reason, legacy preferred shares that were issued at yields substantially higher than the current market yield tend to behave like short-term fixed income securities. Because their costs to the company are so much higher than the current market cost, the investor can be confident that the company will call them in on the call date. Instead of treating them as long-term securities, then, she can treat them as securities that will soon mature at par.

As with a bond, we can separate the risk inherent in preferred shares into credit risk and interest rate risk. The credit risk is the risk that the company will not be able to make the promised payments on the shares. The interest rate risk is the risk that prevailing market interest rates on similar securities will change, causing the price of the security in question to change.

Looking more closely at this second risk, callable securities suffer from a unique disadvantage. When interest rates rise after issuance, they behave like normal fixed income securities. They fall in price, imposing losses on investors, until their market yields increase to a value that’s competitive with the new higher rates. But, as we saw in the earlier example, when interest rates fall after issuance, callable securities are not able to rise to the same extent. That’s because, as they go above par, the potential of a loss on a call is introduced, a loss that will subtract from the total return. To compound the situation, as interest rates fall, a loss on a call becomes more likely, because calling the shares in and replacing them with new ones becomes more attractive to the company, given the better available rates.

Because the company has a call option that it can (and will) use to its own benefit (and to the shareholder’s detriment as its counterparty), preferred shares end up offering all of the potential price downside of long-term fixed income securities, with only a small amount of the potential price upside. When it’s bad to be a long-term bond, they act like long-term bonds. When it’s good to be a long-term bond, they morph into short-term bonds, and get called in. Now, you might ask, given this unfavorable skew, why would anyone want to own callable preferred shares? The answer, of course, is that every security makes sense at some price. Callable preferred shares do not offer the upside of non-callable long-term fixed income securities, but to compensate, they’re typically priced to offer other advantages, such as higher current yields.

Importantly, when a preferred share is trading at a high current yield relative to the market yield, the investor receives a measure of protection from the impact of rising interest rates (or, if we’re focused on real returns, the impact of rising inflation). If interest rates rise, one of two things will happen, both of which are attractive to the shareholder. Either the shares will not be called in, and she will actually get to earn that high current yield over time (which she would not have otherwise gotten to earn), or the shares will be called in, and she will get pulled out of the security, at which point she will be able to take her money and go invest in a better deal.

Preferred Stocks: Assessing the Valuations

The following chart shows the average yield-to-worst (YTW) of preferred stocks alongside the average YTWs of other fixed income asset classes from January 31, 1997 to January 31, 2017, the latest date for which preferred YTW information is available:

Some might challenge this chart on the grounds that preferred stocks are perpetual securities that shouldn’t be compared to bonds, which have maturity dates. The point would be valid if we were evaluating preferred stocks on their current yields. But we’re not. We’re looking specifically at yields-to-worst, which assume that all preferred stocks trading above par get called in on some future date (typically inside of a 5 year period). On that assumption, preferred stocks as a group are not perpetual, but have some average finite term, like bonds. Note that if we were to treat preferred stocks as perpetual securities, the yields shown in the chart would be current yields, which are meaningfully higher than YTWs. For perspective, as of January 31, the current yield for preferreds was 5.53%,versus the 4.78% YTW shown in the chart.

That said, the chart is admittedly susceptible to distortions associated with the fact that the average durations and average credit qualities of the different asset classes may have changed over time, impacting what would be an “appropriate” yield for each of them in any given period. There’s no easy way to eliminate that susceptibility, but I would argue that any potential distortion is likely to be small enough to allow the chart to still offer a general picture of where valuations are.

Let’s look more closely at spreads between preferreds and other fixed-income asset classes. The following two charts show YTW spreads of high-yield and EM USD debt over preferreds. As you can see, spreads have come down substantially and are now well below the average for the period, indicating that preferreds have become cheaper on a relative basis:

The following charts show YTW spreads of preferreds over investment-grade corporates and US treasuries. As you can see, spreads over corporates have increased and are slightly higher than the average, again indicating that preferreds have become cheaper on a relative basis. Versus treasuries, spreads are roughly on the average (with the average having been pushed up significantly by the temporary spike that occurred in 2008).

The above data is summarized in the following table:

The conclusion, then, is that US preferred stocks are priced attractively relative to the rest of the fixed income space. They aren’t screaming bargains by any means, but they look better than the other options. They also look better than US equities, which are trading at nosebleed levels, already well above the peak valuations of the prior cycle.

Now, in comparing yields on these asset classes, we’ve failed to consider an important detail. Preferred dividends are paid out of corporate profits that have already been taxed by the federal government at the corporate level. They are therefore eligible for qualified federal dividend tax rates—15% for most investors, and 23.8% for the top bracket of earners. Bond income, in contrast, is deducted from corporate revenues as interest expense, and therefore does not get taxed by the federal government at the corporate level. It’s therefore taxed at the ordinary income rate–28% for most investors, and 43.4% for the top bracket. Though often missed in comparisons between bond and preferred income, this difference is huge.

The following table shows the current tax-equivalent YTW of preferred shares versus the YTWs of the other fixed income categories. For top earners, the tax advantage gives preferred shares an additional 166 bps in pre-tax yield; for normal earners, an additional 86 bps.

The significance of this advantage should not be understated. With pension assets included, over 60% of all U.S. household financial assets are exposed to income taxation (source: FRB Z.1 L.117.24/L.101.1). Of that 60%, a very large majority is owned by high-net-worth individuals that pay taxes at the top rates. Preferreds effectively allow them to cut those rates in half.

Right now, there’s no shortage of people highlighting the fact that U.S. common equity, represented by the S&P 500 index, is extremely expensive, trading at valuations that are multiple standard-deviations above historical averages. But here’s an interesting piece of information. With respect to preferred equity, the situation is somewhat reversed. In past eras, particularly the period from 1937 to 1964, preferreds traded at very low yields. Today’s yields can easily beat those yields, especially when the tax-advantage, which only came into place in 2003, is taken into account. Prior to 2003, dividends were taxed at normal income rates, including during those periods when capital gains were taxed preferentially.

The following chart shows preferred yields of NYSE stocks from 1910 to 1964 (source: FRED M13048USM156NNBR).

Today’s tax-equivalent yield range of 5.64% to 6.44% is above the 5.05% average from 1910 to 1964, and significantly above the 4.2% average seen from 1937 to 1964, the latter half of the period. I’ve seen many investors pine over the attractive equity valuations seen in the 1940s and 1950s, wishing it were possible to buy at those valuations today. The good news, of course, is that it is possible, provided we’re talking about preferred equity! 😉

Advantages of Financial Preferred Stocks

In market antiquity, preferred shares were very popular. For a fun illustration of their popularity, consider the following advertisement taken from a financial magazine published in 1928. The recommended allocation to preferred stocks is 30%, the same as the bond allocation. Today, financial advisors tend to recommend a much smaller preferred allocation, if they recommend any at all.

The only entities in the current market with any real reason to issue preferred shares are depositary financial institutions–i.e., banks. Preferred shares are attractive to banks because they count as Tier 1 capital under Basel rules. Banks can use them to raise Tier 1 capital and meet minimum Tier 1 capital requirements without having to dilute common shareholders. From a regulatory perspective, the reason preferred shares are treated as capital, and not as debt liabilities, is that a failure to make good on their promised payments will not trigger a default, an event with the potential to destabilize the banking system. Rather, a failure on the part of a bank to pay its preferred shareholders will simply mean that its common shareholders can’t be paid anything. The activation of that constraint will surely matter to common shareholders, but it need not matter to anyone else in the system.

From a shareholder’s perspective, financial preferred shares have a number of unique features that make them attractive. These include:

(1) Counterbalancing Sources of Risk: The credit risk and interest rate risk in a financial preferred share, particularly one issued by a conventional bank, tend to act inversely to each other. To illustrate:

Increased Interest Rate Risk –> Reduced Credit Risk: When interest rates go up, preferred shares face downward price pressure. But, at the same time, higher interest rates tend to increase bank profitability, particularly when the catalyst is an expanding economy. Higher bank profitability, in turn, means a reduction in the risk that banks won’t be able to pay, i.e., a reduction in the credit risk of preferred shares.

Increased Credit Risk –> Reduced Interest Rate Risk: In those situations where credit risk in preferred shares rises–situations, for example, where the banking sector faces losses associated with a weakening economy–interest rates will tend to fall. Considered in isolation, falling interest rates put upward pressure on preferred prices, given that they’re fixed income securities.

Admittedly, in the current environment, one could argue that this effect has already been “maxed out”–i.e., that financial preferred securities are not currently viewed as carrying meaningful credit risk, and that they therefore aren’t likely to see much upward pressure in response to the credit risk “relief” that would come from an improving economy. Regardless of whether or not that’s true, the general point still holds: credit and interest rate risks in financial preferred shares tend to work in opposite directions. We saw that clearly in earlier phases of the current cycle, when credit risk was considered to be meaningful. The shares experienced upward price pressure in response to economic improvement, and were able to rise even as long-term interest rates were rising.

(2) Increased Regulation: With the passage of Dodd-Frank, banks face increased regulation. Increased regulation reduces bank profitability and therefore acts as a drag on the value of common shares. However, it boosts the value of preferred shares, because it makes their risk-reward proposition more attractive.

As a preferred shareholder in a bank, your biggest risk comes from the possibility that the bank might take on too much risk and fail. That risk, if it’s realized, has the potential to bring the value of your investment all the way down to zero. At the same time, your upside in the shares is limited–the most you can realistically expect to make in them over the long-term is the fixed yield that they’re paying you. That yield has no way to increase in response to the profit growth that successful bank risk-taking can produce. This means that if banks are taking on added risk to increase their profitability, you’re exposed to all of the losses and none of the gains–a losing proposition. But in an environment like the current one, where bank risk-taking is closely regulated, and where the regulations are not so onerous as to completely eliminate bank profitability, you end up winning. You continue to earn your promised income, while banks are prevented from putting your investment principal at risk.

Right now, there seems to be a consensus in the market that the election of Donald Trump will lead to significant changes to Dodd-Frank. But that’s hardly a given. Any legislative initiative will have to make it through congress, which is not an easy process. Even if meaningful changes do make it into law, it’s unlikely that the regulatory framework will regress back to what it was pre-crisis. All parties agree that banks need to be regulated to a greater extent than they were during that period.

(3) Strong Balance Sheets: To comply with the upcoming transition to Basel III, banks in the U.S. have had to significantly fortify their balance sheets. Today, their balance sheets are in better shape than they’ve been in several decades. In particular, the relative amount of common equity in U.S. banks, which serves as a potential cushion against preferred losses, is at its highest level since WW2. That means reduced credit risk for bank preferreds.

The best metric to use in quantifying the amount of cushion that bank preferred shareholders have from losses is the tangible common equity ratio. We take a bank’s tangible common equity (tangible assets minus all liabilities minus preferred equity at par) and divide by its tangible assets. The result tells us how much of the bank’s tangible asset base is fully owned by common shareholders. The portion of the balance sheet fully owned by common shareholders is the portion that preferred shareholders will be able to draw from to recover their principal in a liquidation.

The following chart shows the tangible common equity ratios of the big four U.S. banks: JP Morgan Chase, Wells Fargo, Bank of America, and Citigroup. As you can see, the ratios have improved significantly.

Now, to be fair, “bank equity” can be illusory. Even when it maps to something real, it can disappear very quickly during crises. That said, having a a lot of it is still better than having a little, which means that bank preferred shareholders are in a much better position today than they were in prior periods.

(4) Too-Big-To-Fail: Regardless of what anyone might say, “too big to fail” is still a reality. It serves as a backstop on the creditworthiness of bank preferred shares, especially preferred shares issued by the big four money center banks: JP Morgan, Wells Fargo, Bank of America, and Citigroup. We can think of these banks as heavily-regulated, government-backed utilities–ideal candidates for a preferred investment.

$WFC-L and $BAC-L: Two Unique Preferred Issues

Let’s now look at the two securities that will form the focus of the rest of the piece. The first security is a Wells Fargo 7.50% Series L convertible preferred issue (prospectus), ticker $WFC-L, or $WFC-PL, or $WFC/PRL, depending on the quote platform being used. The shares were originally issued as Wachovia shares in the early months of 2008. They became full-fledged Wells Fargo shares, ranking on par with all other Wells Fargo preferred issues, upon Wells Fargo’s acquisition of Wachovia in December of that year (8-K). The par value of each share is $1000, with each share paying out $18.75 per quarter in dividends, or $75 per year, 7.5%. The current market price is around $1220, which equates to a current yield (and YTW) of roughly 6.15%.

The shares are particularly unique–indeed, precious, in my opinion–because unlike almost all other preferred shares trading in the market right now, they are not callable by the company. Instead, they’re convertible. They come with a broad conversion option for the shareholder, and a limited conversion option for the company. For the shareholder, she can convert each share into 6.38 shares of Wells Fargo common stock at any time and for any reason. For the company, if the common shares of Wells Fargo appreciate substantially, it can force that conversion to occur. More specifically, if Wells Fargo common shares, currently priced around $58, exceed a market price of $203.8 (technically: $1000/6.83 * 130%) for 20 days in any 30 day consecutive trading period, then the company can force each preferred share to be converted into common at a 6.38 ratio. If that were to happen, shareholders would get 6.38 common shares, each worth $203.8 in the market, which amounts to a total market value per share of $1300, 130% of par.

It goes without saying that the company is unlikely to be able to convert the shares and get out of the deal any time soon. The market price of Wells Fargo common stock would need to more than triple from its current peak-cycle level. Even if we make optimistic assumptions about the future price growth of such a huge bank–say, 6% per year from current levels–a tripling will take at least another twenty years to occur. That’s great news for owners of the preferred shares–it means that they can expect to receive a tax-advantaged 6.15% yield for at least another 20 years. Additionally, if or when the conversion price is eventually reached, it’s not going to create a loss for current buyers. It’s actually going to create a small gain, because the shares are currently trading at a price below the $1300 that they would effectively be converted into monetarily.

The second security is a Bank of America 7.25% Series L convertible preferred issue (prospectus), ticker $BAC-L, or $BAC-PL, or $BAC/PRL. Like the Wells Fargo shares, these shares were issued in the early months of ’08, at a time when funding for financial institutions was become increasingly tight. In terms of their structure, they’re essentially identical to the Wells Fargo Series L shares, except for the numeric details, shown below:

Now, let’s look more closely at the risk-reward proposition in the shares at current prices.

In terms of reward, the investor will earn a tax-advantaged 6.15% yield (tax-equivalent: 7.26% for 28% earners, 8.28% for top bracket earners) for some unspecified number of years, potentially up to infinity, plus a one-time 5% to 10% gain on a potential conversion decades out. Importantly, because the shares are not callable, they offer the potential for substantial price appreciation–as might occur, for example, if long-term interest rates fall, or if the market discovers additional value in the shares and re-rates their prices. Note that the vast majority of preferred shares in the market are callable, and therefore do not offer investors the same price appreciation potential. As their prices rise, their implied call losses rise, causing their YTWs to quickly drop.

In terms of risk, the shares carry the same risk that any security carries, which is the risk that the market price might fall, for any number of reasons, the most basic of which would be more selling than buying.

Thinking about the risk in fundamental terms, the shares carry the credit risk that Wells Fargo or Bank of America will not be able to pay the promised preferred dividends. In quantifying that risk, Moody’s and S&P have given Wells Fargo preferred shares a BBB rating and a Baa2 rating, respectively, and Bank of America preferred shares a BB+ and Ba2 rating, respectively. Note that these ratings are distinct from the credit ratings of the debt securities of these banks, which obviously have a higher rating.

Personally, I believe the credit risk in the preferred shares of any large money center bank to be very low, for the reasons already stated. But to gauge that risk, we don’t need to rely on speculation. We have an actual historical test case that we can examine: the financial crisis of ’08, which represented the epitome of a worst-case scenario. Notably, the two securities existed before the worst of the ’08 crisis unfolded. Both came through it in perfect health, with all promised dividends paid. Like everything else in the sector, the securities suffered large price drops, but their prices fully recovered.

In addition to credit risk, the shares carry the same risk that any long-term fixed income security carries, which is the risk that long-term interest rates will meaningfully rise, forcing prices to adjust downward to create competitive yields. But these securities, at their current prices, offer three features that can help mitigate that risk, at least partially.

First, at 6.15% (tax-equivalent: 7.26%, 8.28%), their yields and YTWs are already very high, higher than essentially any other similarly rated fixed income security in the market. Conceivably, in a rising rate environment, their prices won’t need to fall by as much in order for their yields to get in line with other opportunities.

Second, if their prices do end up falling over time, they’ll be accumulating a healthy 6.15% yield during the process, helping to offset the losses. That’s much more than the 2.5% to 3% that long-term treasuries will be accumulating.

Third, as discussed earlier, increases in long-term interest rates will tend to increase the profitability of Wells Fargo and Bank of America. The realization of interest rate risk in the shares will therefore have the counterbalancing effect of reducing their credit risk. Granted, the market might not see the shares as carrying any meaningful credit risk right now, and therefore the credit risk “relief” that comes with improved profitability might not help prices very much. But if the shares do not carry any meaningful credit risk, then why are they trading at a yield of 6.15% (tax-equivalent:7.26%,8.28%)? Is that the kind of yield that risk-free securities normally trade at in this market? Obviously not.

Another risk worth mentioning is the risk of forced liquidation. When you buy a preferred security above par, and the underlying company is forced to liquidate, the most you can hope to recover in the liquidation is par, $1000. Buyers at current prices would therefore incur a loss on forced liquidation down to that level. Personally, I don’t see the forced liquidation of either these banks as representing a realistic scenario.

$WFC-L and $BAC-L: Understanding the Valuation Anomaly

With the risks and rewards identified, we can now look more closely at the valuations of the shares. Currently, $WFC-L and $BAC-L are offering current yields and YTWs of 6.15% (the yields and YTWs are the same). That’s 62 bps higher than the 5.53% average current yield of preferred stocks as a group, and 137 bps higher than the 4.78% average YTW of preferred stocks as a group. Unlike the vast majority of shares in the preferred space, however, $WFC-L and $BAC-L aren’t callable, which gives them upside potential that the rest of the space lacks. That difference should cause them to trade at lower yields than the rest of the space–yet we find them trading at higher ones.

Ultimately, there’s no way to make sense of the higher yields. They represent a plain market inefficiency. For conclusive proof of that inefficiency, we can compare the valuations of $WFC-L and $BAC-L to the valuations of other preferred shares from the same issuers. In an efficient market, absent relevant differences in the structures of the shares, the valuations should all be roughly the same, given that the shares represent claims on the same company and rank on par with each other. But that’s not what we’re going to find–they’re all different.

The following table shows all of the currently outstanding fixed rate preferred stock issues of Wells Fargo, each of which ranks on par with every other. Prices are intraday as of February 27, 2017:

As you can see in the above chart, we find the same inefficiencies within the space of Wells Fargo shares. $WFC-L is offering a higher YTW than all of the other issues, and a higher current yield than every other issue except for $WFC-J (a legacy Wachovia issue that has an 8% coupon and that’s essentially guaranteed to be called in at the end of this year, given its high cost to the company–it therefore deserves to be treated differently). Instead of trading at a higher yield than the rest of the space, $WFC-L should be trading at a lower yield, because it’s the only security that’s non-callable, and therefore the only security that has the potential to reward shareholders with a long-term stream of future dividends, as well as meaningful price appreciation as interest rates fall.

Getting inside the head of the market here, I would guess that the thought process being used to justify lower yields for the other shares looks something like this. The other shares can be called, therefore they have lower effective durations, therefore they deserve to trade at lower yields. But this logic misses the crucial fact that the call option belongs to the company, not to the shareholder. It’s only going to be used if using it is in the company’s interests, which is to say, if using it is counter to the interests of the shareholder, the company’s counterparty. There is no scenario in which the existence of the call option will ever be capable of increasing the value of the shares, just as there’s no scenario in which giving someone else a free call option on positions you own could ever make those positions more valuable.

It’s true that in a falling rate scenario, the duration of a callable security will go down. But that’s precisely the kind of scenario where an investor will want to be owning longer-duration securities–securities like $WFC-L that provide a guaranteed stream of dividends out into the future and that are therefore capable of appreciating meaningfully in price.

To see the inefficiency more clearly, let’s compare $WFC-L to $WFC-O. We see the from that table that $WFC-O is offering a 5.23% yield, almost 100 bps lower than $WFC-L’s 6.15% yield. It has a coupon yield of only 5.13%, which is at the absolute low end of what Wells Fargo has been able to issue over the last several years. Because it’s extremely cheap for Wells Fargo to finance, it’s unlikely to ever get called in. The market agrees, which is why it’s trading below par, despite having a call date only 6 months away. Because it’s unlikely to ever get called, we can treat it as a perpetual security. Is 5.23% an appropriate yield for a perpetual security? Maybe, but not with the equally-ranked WFC-L, also a perpetual security, yielding 6.15%!

Now, assume that over the next several years, interest rates go down, breaking below the lows of last summer. $WFC-O will not be able to appreciate in such a scenario because the call option will already be exerciseable. Any move above par ($25) will expose buyers to immediate call losses. Moreover, the company will want to call the security in, because it will be able to refinance at better yields in the market. The situation with respect to $WFC-L, however, is different. It is set to pay a solid stream of sizeable dividends decades out into the future. Given the lack of a call feature, unless the common stock triples, there’s nothing that the company can do to get out of paying those dividends. For that reason, $WFC-L has a full runway on which to appreciate in price should interest rates come down. So while $WFC-O would be stuck at $25 in the scenario, $WFC-L would be able to rise by several hundred points, if not more.

To summarize, then, you have a perpetual security that’s offering a contingent (callable) dividend stream with no price appreciation potential ($WFC-O) trading at a yield almost 100 bps lower than a perpetual security with an equal ranking from the exact same issuer ($WFC-L) that’s offering a guaranteed (non-callable) dividend stream with substantial price appreciation potential. If you’re looking for a case study to disprove the efficient market hypothesis, you have one right there.

Moving on to Bank of America, the following table shows the company’s currently outstanding fixed rate preferred stock issues, each of which ranks on par with every other:

Again, we see the same types of inefficiencies. BAC-L has the highest YTWs, even though, as a non-callable security, it deserves to have the lowest.

Now, as considerate value investors, we need to ask the question. Why are $WFC-L and $BAC-L priced so much more attractively than the rest of the preferred share market? Are we missing something?

The simple answer to the question is that the market for preferred shares contains a large cohort of unsophisticated investors. For that reason, it frequently produces mispricings. In fairness, for all we know, common equity markets–i.e., the regular stock market–may also produce frequent mispricings. But the mispricings would be much harder to conclusively prove, given that there are so many confounding variables associated with that type of investing.

To illustrate, ask yourself, right now, is $AMZN mispriced relative to $AAPL? You can’t know for sure, because you don’t have a reliable way to estimate the likely future cash flows of either company, nor a reliable way to quantify the many risks associated with those cash flows. The question therefore can’t be resolved, except in hindsight, at which point an efficient market guru can easily say, “The market was correctly pricing the securities based on the available information at the time. Hindsight obviously changes the picture.”

With preferred shares, however, we can look at par securities from the exact same issuer, and watch them trade at substantially different yields. Without a justification somewhere in the structure of either security, the mispricings become undeniable. Unfortunately, mispricings in the preferred space cannot be readily corrected through arbitrage (i.e., buying the underpriced shares and shorting the overpriced shares) because the borrow costs on the overpriced shares tend to be prohibitively high. The borrow cost on $WFC-O, for example, is between 10% and 11% annualized, so if you wanted to collect 100 bps annually by shorting $WFC-O and going long $WFC-L, the carrying cost of the trade will end up being 10X that amount.

Now, back to the unanswered question of why the market is currently mispricing these securities. I can think of at least three possible reasons:

Reason 1: Callability Neglect and Par Anchoring

As I insinuated earlier, not everyone participating in the preferred share space understands or properly accounts for the impact of callability. There are uninformed investors who will buy based simply on seeing a high yield, ignoring considerations related to callability. As evidence of that claim, consider two interesting debacles that occured last year in the bank preferred space–the case of Merrill Lynch 6.45% trust preferreds, ticker $MER-M, and the case of Bank of America 6% trust preferreds, ticker $BAC-Z. Last summer, both of these high-cost shares were lazily trading well above their par values, even though they had become callable. The excess in price over par was far greater than any individual future dividend payment could have made up for, yet investors in the space were willing coming in each day and buying them. When the shares did get called in, the net result was bloodshed:

So there you have one likely explanation for why investors might be mispricing the securities–they aren’t paying attention. They go in, for example, and pick $BAC-I over $BAC-L simply because it offers a higher yield, never mind the fact that it becomes callable in a few months and has a current YTW that’s negative.

Another likely explanation is that there are investors that wrongly interpret callability to be a beneficial feature of preferreds, a feature that lowers duration and reduces interest rate risk. Because $WFC-L is not callable, it’s conceptualized as having a higher duration and as being more exposed to interest rate risk. But that’s completely wrong. $WFC-L is no more exposed to interest rate risk than any of the other callable securities (with the limited exception of $WFC-J, which is all but guaranteed to be called in, given its 8% cost to the company). As I emphasized earlier, callability doesn’t protect investors from rising rates because securities don’t get called in when rates are rising (i.e., when corporate financing costs are going up). They get called in when rates are falling (i.e., when corporate financing costs are going down), which is precisely when an investor will not want them to be called in.

We can imagine an unsophisticated investor thinking to himself–“This stock has a call date 3 yrs from now, which isn’t very far away. There’s a decent chance I’ll get my back then, regardless of what Mr. Market decides to do. It’s not a 100 year security, so it’s not like I’m going to be stuck holding it forever.” The problem, of course, is that the security is going to turn into a 100 year security in exactly the kinds of situations where the investor will wish it was a 3 year security. And it’s going to shift back into a 3 year security in exactly the kinds of situations where the investor will wish it was a 100 year security. The investor does not own the option, and therefore the investor should not expect to receive any benefit from it.

On a similar note, I’ve noticed that when the price of a security–say, $WFC-O–trades steadily near or below par, investors tend become more comfortable with it, even when they shouldn’t be. It’s as if they anchor to “par” as a reliable standard of normalcy, fairness, appropriateness–a price that can be trusted. This tendency may help explain why $WFC-L trades so cheaply relative to other $WFC issues. To trade at a fair price relative to the rest of the space, it would have to trade upwards of 50% above par, at $1500, a price that feels excessive, even though it could easily be justified on the basis of relative value.

To be clear, par may be a normal, fair, appropriate, trustworthy price for a security on the date of its issuance–it’s the price, after all, that other presumably intelligent people agreed to pay when they made the initial investment. But once that date passes, and conditions change, the question of how close or far a given price is to or from it is entirely irrelevant.

Reason 2: Large Outstanding Market Supply

The point I’m going to make here is more complex, but also more interesting, so you’re going to have to be patient and bear with me.

All else equal, a larger outstanding market supply of a security (price times share count) will tend to put downward pressure on its price. This fact helps explain why $WFC-L and $BAC-L trade so cheaply on a relative basis. As shown in the earlier tables, their outstanding market supplies–measured in dollar terms at $5B and $7B, respectively–are extremely large relative to the outstanding market supplies of the other preferred issues.

To understand why supply matters, recall that as you increase the outstanding market supply of a security–for example, by issuing large quantities of new shares–you are necessarily increasing the total “amount” of the security floating around in the market, and therefore the total “amount” sitting in investor portfolios, because every issued share has to it someone’s portfolio at all times. Trivially, by increasing the total “amount” of the security contained in investor portfolios, you are also increasing the total “amount” of it that investors will randomly attempt to sell in any given period of time (and here the selling can be for any reason: because the investor is concerned, because a better investment has been found, because the cash is needed to fund some other activity–whatever, it doesn’t matter). The point is strictly intuitive–more outstanding units of a security in investor portfolios means more units that get randomly sold every day, and every hour, and every minute, as investors move their portfolios around in response to their own whims and fancies.

That selling is a flow quantity, so we refer to it as attempted selling flow; all else equal, it increases whenever supply increases. Now, it’s a truism of markets that, for a price equilibrium to be reached, attempted buying flow in a security has to match attempted selling flow in that security. If attempted buying flow is less than attempted selling flow, prices will not stay put. They will get pushed lower.

So ask yourself this question. As the outstanding market supply of a security goes up, and therefore as the amount of attempted selling flow in that security goes up, does the amount of attempted buying flow also go up–automatically, spontaneously, simply to stay even with what’s happening elsewhere? No. There’s no reason for attempted buying flow to go up simply in response to an increase in the outstanding market supply of a security. But that flow has to go up, otherwise the attempted flows will not match, and prices will fall. So what happens? Prices fall. The security trades more cheaply. By trading more cheaply, it draws in interest from investors, resulting in an increase in attempted buying flow to match the increased attempted selling flow and return the price to an equilibrium at some new lower level.

Empirically, we see that big behemoth companies, with large supplies of market equity for investors to hold in their portfolios, tend to trade more cheaply than smaller ones, all else equal. You can look look at $AAPL, with its massive $716B market value, as a good example–investors lament its cheapness all the time: “It has a P/E of 10 ex-cash!” But why do big behemoth companies like $AAPL trade more cheaply? Some would say it’s because their potential future growth is constrained–but that can’t be the only reason. In my view, a significant contributor is the sheer size of their market capitalizations, the enormous outstanding dollar amounts of their equity that investors have to willingly take into portfolios. The the interest to do that–i.e., take in that large supply of equity as a position in a portfolio–isn’t always going to be there, which is why big behemoths sometimes have to become cheap, so that they they can attract more willing buyers and more willing owners.

As a company like $AAPL grows in market capitalization, it becomes a larger and larger portion of investor portfolios. A larger dollar amount of it is attempted to be sold every day. But does the growing market capitalization also cause a larger amount of it to be attempted to be bought every day? No. The buy side of the equation isn’t affected by supply–it has no way to know that supply is increasing. And so the security sees more selling demand than buying demand, until it becomes cheap enough to attract sufficient buying demand to correct the imbalance. That’s the dynamic. Now, to be fair, as a company like $AAPL grows in size, reaching ever higher market capitalizations, it will typically become more popular, more talked about, more visible to market participants, and so on. More people will hear about it, know about it, and therefore more people will wake up in the morning and randomly decide “Hey, I want to own that stock.” That effect–the increase in popularity and visibility that occurs alongside equity growth–can bring with it an increase in attempted buying flow, an increase that can help quench the increased attempted selling flow that will naturally arise out of the increased market supply of the equity. If that happens, the company, as a big behemoth, may not need to become as cheap, or cheap at all.

But when we’re talking about two obscure preferred stock issues that very few people even know about, preferred stock issues that didn’t arrive at their current market sizes through the growth of an underlying business, but that were instead dumped on the market en masse during a crisis-era fundraising effort, their attempted buying flow isn’t going to be able to rise to the necessary levels in the same way, i.e., by an increase in popularity or visibility or whatever else comes with growth. The only way they’ll see sufficient attempted buying flow to match the large attempted selling flow that they’ll naturally face is if they trade more cheaply, cheap enough to come up more frequently on value screens and attract attention from bargain-seeking investors. And that’s exactly how we see $WFC-L and $BAC-L trade–cheap enough to draw interest from those looking for a deal.

For a fascinating illustration of supply effects working in the other direction, driving prices to irrationally high levels, consider the curious case of Kansas City Southern non-cumulative 4% preferred shares, which have a par value of $25 and trade on the NYSE as $KSU-, $KSU-P or $KSU/PR. A total of 649,736 of the shares were issued in a $16.24MM IPO that took place in November of 1962, at a time when preferred shares tended to trade at very low yields. Shortly thereafter, around 400,000 of the shares were eliminated in a tender offer, leaving 242,170 shares leftover. At par, those shares represent a total dollar market supply of $6.05MM–a tiny supply by any measure. Because they were issued with no call feature, they still trade in the market to this day. They have no way to leave the market, because they don’t mature, convert, or have a call feature.

Now, recall that unlike common dividends, preferred share dividends and preferred share prices don’t have the potential to grow with the economy over time. Consequently, without new issuance, their outstanding market supplies (price times share count) can’t grow with the economy over time. For that reason, the market supply of $KSU preferreds has stayed constant at roughly $6.05MM for over 50 years , even as the market value of the rest of the asset universe, to include the economy’s money supply, has increased by a factor more than 30X. The end result is that $KSU preferreds have become the “Honus Wagner T206” of the preferred share market. They are unique preferred shares that, through a quirk, have been rendered incredibly scarce. Their scarcity causes them to trade at irrationally high prices.

One would think that in the current environment, at only a 4% coupon, the shares would trade significantly below par. But, for reasons that make no rational sense whatsoever, they trade at a strong premium to par, at price of 28.75 and a yield of 3.45%. For perspective, that’s only 45 bps above 30-yr treasuries, for a perpetual fixed income security that’s subordinate to BBB- rated corporate debt!

So you have $WFC-L preferreds, rated BBB, offering a yield of 6.15%, and then you have $KSU- preferreds, with no rating, issued by a company whose senior debt is rated BBB-, offering a yield of 3.45%, 260 bps lower–in the same market, on the same exchange. The clearest available explanation for this crazy price outcome is supply: the total dollar amount of market value in $WFC-L, an amount that has to find a home in someone’s portfolio at all times, is roughly 1000X larger than the total amount of $KSU- to be held. Granted, there could be other unmentioned forces at work–$KSU- might have a few very large shareholders who refuse to sell and who contribute to an even tighter shortage. But those forces are highly-likely to somehow involve supply considerations as well, given that no fundamental information about the shares could justify such a ridiculous valuation.

Reason 3: $1000 Par Value, Convertibility, Index Exclusion

A third reason for the potential cheapness of $WFC-L and $BAC-L is the fact that the shares exhibit unique properties that make them less likely to see buying demand from the usual sources. The shares trade at an unusually high par value, $1000, versus the normal $25. They have a complicated conversion-to-common feature, one that can be difficult to clearly decipher from the legalese in the prospectus. These factors might steer certain investors away from them–in particular, income-seeking retail investors, who constitute a significant portion of the preferred market.

More importantly, because of their differences from normal preferred securities ($1000 par, convertible, etc.), they are excluded from most preferred stock indices. As a consequence, you don’t see them represented in popular preferred stock ETFs. $PSK, $PGX, and $PGF, for example, all exclude them. I’ve gone through all of the popular preferred stock mutual funds, and at least as of last year, only one of them owned either of the two shares–in that case, it was $WFC-L. The largest preferred ETF index–$PFF–also owns $WFC-L, but doesn’t own $BAC-L. Note that if it did own $BAC-L at the right index ratio, the shares would be roughly a 4.25% position, the largest in the index, given the large market supply of $BAC-L outstanding.

When we consider these three factors together–first, the possibility that investors might be ignoring the call feature or misinterpreting it as some kind of a duration-related advantage, second, the fact that, in relative terms, there’s a very large outstanding market supply of the securities to be held, weighing down on their prices, and third, the fact that the securities have unique features that make them less likely to see interest from the usual sources of preferred buying interest–the depressed valuations start to make more sense. Admittedly, there’s no obvious catalyst to remove the factors and lift the valuation–but no catalyst is needed. Investors can earn an attractive return in the securities by simply owning them and collecting their outsized yields, paying no mind to whether the market price ever catches up.

Conclusion

In conclusion, preferred stocks are reasonably valued relative to the rest of the market and relative to their own past history, especially when their special tax advantages are taken into consideration. Within the preferred stock space, two unique securities–$WFC-L and $BAC-L–represent very attractive value propositions: 6.15% yields (tax-equivalent to 7.26% and 8.28% for 28% and top bracket earners, respectively), very little credit risk, no call risk, meaningful price appreciation potential, and decades worth of dividends still to pay. In an investment environment like the one we’re living in, where almost everything looks terrible, you have to take what you can get.

Disclosure: I am long $WFC-L and $BAC-L. Nothing in this piece should be interpreted as a recommendation to buy or sell any security. I make no warranty as to the accuracy or completeness of any of the information or analysis presented.

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Let’s suppose that you have money on deposit in a bank, in some kind of checking or savings account. It’s paying you 2.5% per year, which isn’t something you can easily get in 2017, but something that would have been possible several years ago. As a friend with lots of advice to give, I come up to you and strike up the following conversation:

Me: “Why are you tying up your money in a bank for such a low return?”

You: “But I’m not tying it up. I can still use it if I need to. I may have to pay a penalty, but it’s still there for me to access.”

Me: “Oh no, it’s not there.”

You: “How is it not there?”

Me: “The bank loans it out to people. So it’s not there for you to access. They keep a small portion on reserve that they can give out in case people want to withdraw money, but if there’s ever a situation where a sufficient number of people lose confidence in the bank and try to get their money out at the same time, the money’s not going to be there. You’re going to be screwed.”

You: “Well, what should I do instead?”

Me: “You should keep the money in a safe. When you keep it in a bank, you’re taking on risk for a paltry potential return. That’s stupid.”

Let’s neglect for a moment any potential banking system misconceptions revealed in this conversation. The question I want to ask is: does it make sense, for reasons of convenience and for the potential to earn a few hundred additional basis points of interest, to keep money in a bank rather than in a personal safe? Assuming the bank is soundly managed and has a fundamentally solvent balance sheet, the only risk to your money is the possibility that everyone might rush to take money out of it at the same time. There’s a network of confidence that buffers against that possibility. Nobody expects people to panic and try to take money out, therefore a people don’t panic and try to take money out, and the system holds up. Assuming there’s strength and stability in the network of confidence, it can make perfect sense to opt for the added convenience and the extra 2.5% over cash.

In our modernized banking system, this point goes even farther. The network of confidence is dramatically strengthened by the fact that there’s government insurance on deposits, and also by the fact that there’s a central bank with a charter to provide liquidity to solvent institutions that need it. There’s essentially no possibility that a financially sound bank could ever be destroyed by a bank run. And so if your choice is to keep money in a safe or earn 2.5% at such a bank, you should always choose the bank option.

There are valuable parallels here to asset markets, particularly in environments like the current one where short-term rates are expected to remain very low over the long-term. I’m going to explain those parallels in a bit, but before I do that let me first clarify some concepts that I’m going to make reference: financial asset and intrinsic value.

A financial asset is an entity that pays out a stream of cash flows to the owner over time. The intrinsic value of a financial asset is the maximum price that an investor would be willing to pay to own the stream if she enjoyed no liquidity in owning it–that is, if she were required to hold it for the entirety of its life, and couldn’t ever take her money out of it by selling it to someone else. To illustrate the concept, consider a share of the S&P 500. In essence, each share is a claim on a dividend stream backed by the earnings of 500 elite U.S. companies. The stream grows in real terms over time because some of the earnings are retained to fund acquisitions and business expansions, which increase the cash flows and dividends that can be paid out in future periods. Last year, each share of the S&P 500 paid out around $45 in dividends. Next year, the number might be $46, the year after that, maybe $47, and so on. There will be sudden drops now and then, but the general trend is upward.

Obviously, estimates of the intrinsic value of a given security will be different for different investors. A useful way to estimate that value for a security you own is to ask yourself the question: what is the most you would be willing to pay for the security if you couldn’t ever sell it? Take the S&P 500 with its $45 dividend that grows at some pace over the long-term–say, 2% real, plus or minus profit-related uncertainty. What is the most that you would be willing to pay to own a share of the S&P 500, assuming you would be stuck owning it forever? Put differently, at what ratio would you be willing to permanently convert your present money, which you can use right now to purchase anything you want, including other assets, into a slowly accumulating dividend stream that you cannot use to make purchases, at least not until the individual dividends are received?

When I poll people on that question, I get very bearish answers. By and large, I find that people would be unwilling to own the current S&P 500 for any yield below 5%, which corresponds to a S&P 500 price of at most 1000. The actual S&P trades at roughly 2365, which should tell you how much liquidity–i.e., the ability to take out the money that you put into an investment–matters to investors. In the case of the S&P 500, it represents more than half of the asset’s realized market value.

Now, here’s where the parallel to banking comes into play. As with a bank, a market’s liquidity is backed by a network of confidence among its participants. Participants trust that there will be other participants willing to buy at prices near or above the current price, and therefore they themselves are willing to buy, confident that they will not lose access to their money for any sustained period of time. Their buying, in turn, supports the market’s pricing and creates an observable outcome–price stability–that reinforces trust in it. Because the investors don’t all rush for the exits at the same time, they don’t have a need to rush for the exits. They can rationally collect the excess returns that the market is offering, even though those returns would be insufficient to cover the cost of lost liquidity.

When the network of confidence breaks down, you end up with a situation where people are holding securities, nervous about a possible loss of access to their money, while prevailing prices are still way above intrinsic value, i.e., way above the prices that they would demand in order to compensate for a loss of liquidity. So they sell whatever they can, driving prices lower and lower, until confidence in a new price level re-emerges. Prices rarely go all the way down to intrinsic value, but when they do, investors end up with generational buying opportunities.

Recall that in our earlier example, you have two options. You can hold your money in a safe, or you can hold it in a bank. The safe gives you absolute security–no possibility of ever losing access to the money. The bank gives you a 2.5% extra return, plus convenience, all in exchange for risk to your access. Granted, you can get your money out of the bank whenever you want–but only if the network of confidence that backs its liquidity remains intact. Because you believe that the network of confidence will remain intact, you choose the convenience and the added return. Our modernized banking system simplifies the choice dramatically by externally bolstering the network through the use of mutual insurance and the designation of a lender of last resort. And so there’s not even a question as to whether you should take the convenience and additional 2.5% return that the bank is offering. You should take any extra return at all, all the way down to zero, because there’s essentially no risk that the network that backs your access to the money will ever break down.

Investors face a similar choice. They can hold their money in cash, and earn a low return–in the current case, 0%–or they can purchase an asset. The cash gives them absolute, unrestricted access to their money at all times, whereas the asset gives them imperfect access, access that’s contingent, at least in part, on the sustained preferences and expectations of other investors. In compensation for that risk, they get an extra return, often a large extra return.

The question comes up: in a low rate world, with assets at historically high valuations, offering historically low returns, what should investors do? Should they opt to own assets, or should they hold cash? The point I want to make in all of this is that to answer the question, we need to gauge the likely strength and sustainability of the market’s network of confidence amid those stipulated conditions. We need to ask ourselves whether investors are likely to remain willing to buy at the high valuations and low implied returns that they’ve been buying at. If the conclusion is that they will remain willing, then it makes all the sense in the world to buy assets and continue to own them. And if the conclusion is that they won’t remain willing, that something will change, then it makes all the sense in the world to choose hold cash instead.

If we’re living in a low-rate world, and our only option other than holding cash is to buy the S&P at 30 times earnings, or a 30 year treasury at 2%, or whatever other shitty deal is on offer, and you ask me what we should do, I can only answer the question by asking whether there will continue to be a ready supply of buyers at those valuations into the future. And the point is, regardless of what “historical averages” have to say about the matter, there may continue to be! As always, path is crucial. If valuations have arrived at their current levels through short-term excitement and mania, then we should be more suspicious of their forward-looking sustainability. The network of confidence sustaining those valuations is likely to be fickle and to eventually break down. But if prices have gradually moved to where they are over a long period of time, in response to legitimate secular market forces and conditions, if participants have had sufficient time to grow accustomed to them, to psychologically anchor to them, such that they see them as normal and appropriate, then the basis for questioning their sustainability isn’t going to be as strong.

It’s important to remember that as long as cash is yielding zero or something very low, there’s no arbitrage to force asset prices lower, no dynamic to force them to conform to some historically observed level or average. They can go as high as they want to, and stay as high as they want to, provided investors are able to develop and retain the confidence to buy at those levels. Note that the same point doesn’t hold as readily in the other direction, when considering how low prices can go. That’s because financial assets have intrinsic value. Below that value, they’re worth owning purely for their cash flow streams, regardless of the prices at which they can be sold. The market can take those prices all the way to down to zero, they’ll still be worth owning as incoming cash flow streams.

People won’t like to hear this, but in the same way that policymakers have introduced structures and practices into the banking system designed to bolster the networks of confidence that sustain banking liquidity, policymakers are capable of introducing structures and practices into financial markets that bolster the networks of confidence that sustain market liquidity. For example, in order to prevent sharp drops that would otherwise be economically harmful, policymakers can use public money to buy equities themselves, providing a direct backstop. Or if that’s not an option legally, they can talk up financial markets, accompanying the talk with whatever policy tools market participants find compelling. If it’s the case, as some argue, that policymaker approaches around the world are evolving in that direction, then that provides yet another basis for valuations to get pushed higher, just as it provided a basis in our earlier example for a depositor to keep money in a bank despite being paid a paltry rate.

It’s often said that bank solvency is an unhelpful concept, given that a bank’s ability to survive is often determined more by its liquidity condition than by anything happening on its balance sheet. Every bank can survive a solvency crisis if given enough liquidity, and every bank can be put into a solvency crisis if starved of enough liquidity. Some would argue, for example, that Lehman failed not because it was truly insolvent, if that even means anything, but because the Fed, right or wrong, refused to lend to it when no one else would. It couldn’t survive the crunch it faced, so it folded. In hindsight, we conclude that it was insolvent. But was it? It’s something of a stretch, but we can find an analogy here to stock market valuation. Every stock market, in hindsight, is seen as having been “expensive” or in a “bubble” when the network of confidence that holds it together breaks down, i.e., when people panic and sell out of it, driving it sharply lower. And every stock market, in hindsight, is seen as “fairly valued” when it suffers no panic and slowly appreciates as it’s supposed to do.

With respect to equity markets in particular, I’ll end with this. If we want to get in front of things that are going to break a market’s network of confidence and undermine people’s beliefs that they’ll be able to sell near or above where they’ve been buying, we shouldn’t be focusing on valuation. We should be focusing instead on factors and forces that actually do cause panics, that actually do break the networks of confidence that hold markets together. We should be focusing on conditions and developments in the real economy, in the corporate sector, in the banking system, in the credit markets, and so on, looking for imbalances and vulnerabilities that, when they unwind and unravel, will sour the moods of investors, bring their fears and anxieties to the surface, and cause them to question the sustainability of prevailing prices, regardless of the valuations at which the process happens to begin.

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In this piece, I’m going to introduce a simplified model of a fund market, and then use the model to illustrate certain important concepts related to the impact of the market’s ongoing transition from active to passive management. Some of the concepts have already been discussed in prior pieces, others are going to be new to this piece.

Share ownership by individuals is not allowed. The only way to own shares is to invest in a fund, and there are no funds to invest in other the 1,000 funds already specified. All shares in existence are held somewhere inside those funds.

The passive fund is required to target a 100% allocation to equities over the long-term, holding shares of each company in relative proportion to the total number of shares in existence.

The active funds are required to target a 95% allocation to equities over the long-term. They are free to implement that allocation in whatever way they want–i.e., by holding shares of whatever companies they prefer. The 95% number is chosen because it leaves the active funds with enough cash to trade, but not so much cash as to appreciably detract from their returns. Note that from here forward, when we refer to the “returns” of the active funds, we will be referring to the returns of the portion of the funds that are actually invested in the market, not the overall returns of the funds, which will include the returns of a certain amount of cash held for the purposes of liquidity.

The passive fund and the group of 999 active funds each represent roughly half of the overall market, a fact represented in the identical sizing of the grey boxes in the schematic above.

Each active fund charges an annual management fee of 1%. The passive fund is publicly-administered and charges no fees.

We can separate the market’s valuation into two dimensions: (1) absolute valuation and (2) relative valuation.

(2) Relative Valuation: Valuation of companies in the market relative to each other.

If we know these two dimensions, then, assuming we know the fundamentals of the underlying companies (earnings, dividends, etc.), we can infer the exact prices of all shares in the market.

Importantly, the two dimensions of the market’s valuation are controlled by two distinct entities:

The fund investors control the market’s absolute valuation through their net cash injections and withdrawals (see green and red arrows, respectively). They cannot control the market’s relative valuation because they cannot trade in individual shares.

The active funds control the market’s relative valuation through their buying and selling of individual shares. They cannot control the market’s absolute valuation because they are not allowed to try to increase or decrease their long-term allocations to equities.

The passive funds control nothing, because they have no freedom in any aspect of their market behaviors. They must deploy 100% of any funds they receive into equities, and they must buy and sell shares so as to establish positions that are in exact relative proportion to the supply outstanding.

Suppose that an investor sends new cash into a fund–either the passive fund or one of the 999 active funds–and that everything else in the system remains unchanged. The receiving fund will have an allocation target that it will have to follow. It will therefore have to use the cash to buy shares. But the receiving fund cannot buy shares unless some other fund sells shares. That other fund–the selling fund–will also have an allocation target that it will have to follow. It will therefore have to use the cash from the sale to buy shares from yet another fund, which will have to use the cash from the sale to buy shares from yet another fund, which will have to use the cash from the sale to buy shares from yet another fund, and so on. Instead of sitting quietly in the hands of the fund that it was injected into, the cash will get tossed around from fund to fund across the market like a hot potato.

How long will the tossing around of the hot potato (cash) last? At a minimum, it will last until prices rise by an amount sufficient to lift the aggregate equity capitalization of the market to a level that allows all funds to be at their target equity allocations amid the higher absolute amount of cash in the system. Only then will an equilibrium be possible.

To illustrate, suppose that each fund in the system is required to target an allocation of 95% equity, and 5% cash. Consistent with that allocation, suppose that there is $95MM of aggregate market equity in the system, and $5MM of aggregate cash. (95MM/$100MM = 95% equity, and $5MM/$100MM = 5% cash, so there’s a sufficient supply of each asset for every fund to satisfy its allocation mandate.) Suppose that investors then inject $5MM of new cash into the system, raising the total amount of cash to $10MM. That injection will throw the funds’ allocations out of balance. As a group, they will find themselves under-invested in equity relative to their targets, and will therefore have to buy shares. They will have to persist in that effort until prices rise by an amount sufficient to increase the system’s aggregate equity market capitalization to $190MM, which is the only number that will allow every fund to have a 95% allocation to equity amid the higher amount of cash ($10MM) in the system. ($190MM/$200MM = 95% equity, and $10MM/$200MM = 5% cash, leaving a sufficient supply of each asset for every fund to satisfy its allocation mandate.)

When cash is removed from the system, the same process takes place in reverse–prices get pulled down by the selling until the aggregate equity market capitalization falls to a level that allows the funds to be at their allocation targets amid the lower absolute amount of cash in the system.

Now, the process by which investor flows drive valuations in our hypothetical market is subject to the same natural feedbacks seen in any real market. As prices go up, the market’s valuation and implied future return becomes less attractive, therefore fewer investors send cash in, more investors take cash out, and prices see downward pressure:

As in any real market, there are situations in which this natural negative feedback can give way to a different kind of positive feedback, where rising prices reflexively lead to greater optimism and confidence, fueling increased buying, decreased selling, and therefore further price increases:

I highlight the details here simply to point out that the feedback processes governing prices in our hypothetical market are no different from the feedback processes that govern prices in real markets. The only difference is in the artificial “fund” structure that we’ve imposed, a structure that helps us separate out and explore the different components of price formation.

Relative Valuation: Driven by Active Fund Preferences

Active funds are the only entities in the system that have the ability to express preference or aversion for individual shares at specific prices. They are therefore the only entities in the system with direct control over the valuation of individual shares relative to each other.

If an active fund skillfully arbitrages the prices of individual shares–buying those that are priced to offer high future returns and selling those that are priced to offer low future returns–it will earn a clear micro-level benefit for itself: an excess return over the market. But will its successful arbitrage produce any macro-level benefits for the larger economy?

To answer the question, imagine a society where coins are the primary form of money, and where people generally hold coins in their pockets. Suppose further that in this society, there are a select group of careless people who fail to buy new pants on a recurring basis, and who therefore end up with holes in their pockets. As these people walk around the society, they unknowingly drop coins on the floor, leaving coins laying around for other passers-by to pick up and profit from. A savvy individual recognizes the profit opportunity asssociated with the “mistakes” these coin-droppers are making, and develops a way to skillfully “arbitrage” them. Specifically, he builds a super-whamodyne metal detector, which he uses to go on sophisticated coin hunts throughout the society. With this super-whamodyne metal detector, he is able to pick up falling and hidden coins much faster than anyone else, and therefore generates an outsized profit for himself.

Clearly, his coin-hunting activities will generate a micro-level benefit for him. But, aside from possible street cleanliness (fewer coins laying around?), are there any compelling macro-level benefits that will be generated for the overall society? No. Any “profit” that he earns in finding a given coin will be the mirror image of the loss incurred by whoever dropped it, or whoever failed to pick it up in front of him. His effort will benefit him, but the benefit will always occur alongside corresponding losses or missed gains for others. The system as a whole will see no net gain. From a macro-level perspective, the resources expended in the effort to build the super-whamodyne metal detector, and lug it all around the society in search of treasure, will have been completely wasted.

We can think of market arbitrage in the same way. Some market participants make mistakes. Other market participants expend vast resources trying to arbitrage those mistakes, with an emphasis on getting their first, in order to capture the profit. No value is generated in the process; rather, value is simply transferred from the mistake-makers to the arbitrageurs, just as it was transferred from the coin-droppers to the coin-hunter. From a macro-level perspective, the resources expended in the effort end up being wasted.

Now, to be fair, this argument neglects the fact that prices in a market impact capital formation, which in turn impacts an economy’s resource allocation. When a money-losing, value-destroying business is given an undeservedly high price, it is able to raise capital more easily, and is therefore more able to direct additional economic resources into its money-losing, value-destroying operation, where the resources are likely to be wasted. Conversely, when a profitable, value-generating business is given an undeservedly low price, it is less able to raise capital, and is therefore less able to direct economic resources into its profitable, value-generating operation, where they would otherwise have been put to beneficial economic use.

Personally, I tend to be skeptical of the alleged relationship between equity prices and capital formation. Corporations rarely fund their investment programs through equity issuance, and so there’s no reason for there to be any meaningful relationship. This is especially true for the mature companies that make up the majority of the equity market’s capitalization–companies that comprise the vast majority of the portfolio holdings on which active management fees get charged.

To illustrate the point with an example, suppose that the market were to irrationally double the price of Pepsi $PEP, and irrationally halve the price of Coke $KO. Would the change have any meaningful effect on the real economy? In a worst case scenario, maybe $PEP would divert excess income away from share buybacks towards dividends, or arbitrage its capital structure by selling equity to buy back debt. Maybe $KO would do the opposite–divert excess income from away dividends towards share buybacks, or arbitrage its capital structure by selling debt to buy back equity. Either way, who cares? What difference would it make to the real economy? For the shift to impact the real economy, it would have to be the case that money used for share repurchases and dividends and other types of financial engineering is deployed at the direct expense of money used for business investment, which evidence shows is not the case, at least not for large companies such as these. The companies make the investments in their businesses that they need to make in order to compete and profitably serve their expected future demand opportunities. Whatever funds are left over, they return to their shareholders, or devote to financial arbitrage.

Many investors believe that the current equity market is excessively expensive, having been inflated to an extreme valuation by the Federal Reserve’s easy monetary policy. Let’s assume that the most vocal of these investors are right, and that stocks in the market are at least twice as expensive as they should be. The Fed, then, has doubled the market’s valuation–or alternatively, has halved the equity funding costs of corporations. Ask yourself: is this alleged “distortion” leading to excessive corporate investment? No, not at all. If the current economy were experiencing excessive corporate investment, then we would be experiencing an inflationary economic boom right now. But we’re experiencing nothing of the sort–if anything, we’re experiencing the opposite, a period of slumpy moderation, despite being more than 7 years into an expansion. That’s because, contrary to the Fed’s better intentions, the transmission mechanism from share prices to real investment is weak.

Absolute and Relative Valuation: Samuelson’s Dictum

The price dynamics seen in our hypothetical market are obviously different from the price dynamics seen in real markets. In real markets, individual investors are allowed to invest directly in individual shares, which allows them to directly influence relative valuations inside the equity space. Similarly, in real markets, many of the active funds that invest in equities–for example, hedge funds–are able to significantly vary their net exposures to equities as an asset class. This ability allows them to directly influence the equity market’s absolute valuation.

With that said, there’s probably some truth to the model’s implication. Individual investors (as well as the first-level custodians that manage their money, e.g., RIAs) probably exert greater control over the market’s absolute valuation. That’s because they directly control flows into and out of investment vehicles that have no choice but to be fully invested in equities–e.g., active and passive equity mutual funds and ETFs. Conversely, they probably exert less control over the relative valuation of shares inside the equity market, because they’re less likely to be the ones directly speculating inside that space, opting to rely on the available investment vehicles instead.

In contrast, the professional managers that operate downstream of individual investor flows, and that manage the various investment vehicles that provide those investors with equity exposure, probably exert less control over the market’s absolute valuation. That’s because when flows come into or go out of their vehicles, they have to buy and sell, which means they have to put the associated buying and selling pressures somewhere into the market. They cannot opt to “hold” the pressure as a buffer–they have to pass it on. Conversely, they probably exert greater control over the relative valuation of shares inside the market, given that source investors often step aside and leave the task of making relative trades in the market to them, based on their expertise.

This fact may be the reason for Samuelson’s famous observation that markets are more efficient at the micro-level than at the macro-level. If micro-level decisions–e.g., decisions about which specific companies in the equity market to own–are more likely to be made by professionals that possess experience and skill in security selection, then we should expect markets to be more efficient at the micro-level. Conversely, if macro-level decisions–e.g., decisions about what basic asset classes to invest in, whether to be invested in anything at all, i.e., whether to just hold cash, and how much cash to hold–are more likely to be made at the source level, by the unsophisticated individuals that allocate their wealth to various parts of the system, individuals that are in no way inclined to optimize the timing of the flows they introduce, then we should expect markets to be less efficient at the macro-level.

We should note, of course, that the concept of efficiency is far more difficult to make sense of at the macro-level, where the different assets–cash, fixed income, and equities–are orthogonal to each other, i.e., of a totally different kind. The advantages and disadvantages associated with holding them cannot be easily expressed in each other’s terms.

To illustrate, a share of Google $GOOG and a share of Amazon $AMZN are the same general kind of asset–an equity security, an intrinsically-illiquid stream of potential future dividends paid out of future free cash flows. Because they are the same general kind of asset, it is easier to express the value of one in terms of the value of the other. If, at every point into the future, a $GOOG share will generate double the free cash flow of the $AMZN share, then it has double the value, and should be double the price; similarly, if it will generate half the free cash flow, then it obviously has half the value, and should be half the price.

A share of Google $GOOG and a dollar bill, in contrast, are not the same kind of asset–one is an equity security, an intrinsically-illiquid stream of future monetary payments, the other is fully-liquid present money, in hand right now for you to use in whatever way you please. Because they are not the same kind of asset, there is no easy way to put the two asset types together onto the same plane, no necessary, non-arbitrary ratio that one can cite to express the value that one posseses in terms of the other–e.g., 710 dollars for every $GOOG share. But that is precisely what it means to “value” them.

The Active Management Fee: Can it Be Earned?

Now, let’s be fair. In working to establish “correct prices”, active funds in a secondary market do provide macro-level benefits for the economy. It’s just that the benefits are small, frequently exaggerated in their actual economic impacts. As compensation for the work they perform in those efforts, the funds charge a fee–in our hypothetical example, the fee was 1% of assets. To earn that 1% fee, the funds need to outperform the market by 1% before fees. As a group, is it possible for them to do that?

The temptation is to say no, it is not possible. The passive fund is holding the market portfolio. Since the passive fund plus the collection of active funds equals the overall market, it follows that the active funds, collectively, are also holding the market portfolio. Given that the two segments of the market–passive and active–are holding the same portfolios, it’s logically impossible for one segment to outperform the other. In previous pieces, we called this observation, attributable to William Sharpe, “The Law of Conservation of Alpha.” Aggregate alpha in a market must always sum to zero.

The Law of Conservation of Alpha seems to leave us no choice but to conclude that the active funds in our hypothetical system will simply underperform the passive fund by the amount of their fees–in the current case, 1%–and that the underperformance will continue forever and ever, never being made up for. But if that’s the case, then why would any rational investor choose to invest in active funds?

Imagine that there are two asset classes, A and B, and that you have the option of investing in one or the other. Suppose that you know, with absolute certainty, that asset class B is going to underperform asset class A by 1%. Knowing that fact, why would you choose to invest in asset class B over asset class A? Why would you choose to invest in the asset class with the lower expected return?

It makes sense for investors to accept lower returns in exchange for lower amounts of risk. But, in this case, the group of active funds are not offering lower risk in comparison with the passive fund. They are offering the exact same risk, because they are holding the exact same portfolio. In fact, there’s a relevant sense in which the active funds, considered individually, are offering additional risk in comparison with the passive fund–specifically, the additional risk of underperforming or outperforming the benchmark. To be fair, that risk may not be a clear net negative in the same way that volatility is a net negative, but it certainly isn’t a net positive, and therefore it makes no sense for investors to throw away 1% in annual return, every year, year after year, in exchange for the highly dubious “privilege” of taking it on.

What we have in our hypothetical market is an obvious arbitrage–go with the passive fund, and earn an extra 1% per year in expected return, with no strings attached. As investors become increasingly aware of that arbitrage, we should expect them to shift their investments out of the active funds and into the passive fund, a transition that is taking place in real markets as we speak. Our intuitions tell us that there should be adverse consequences associated with the transition. As more and more investors opt to free-ride on a passive approach, pocketing the 1% instead of paying it, we should expect there to be negative impacts on the market’s functioning.

In a previous piece, I argued that there were impacts on the market’s functioning–but that, surprisingly, they were positive impacts. Counter-intuitively, the transition out of active funds and into passive funds makes the market more efficient in its relative pricing of shares, because it preferentially removes lower-skilled players from the active segment of the market, leaving a higher average level of skill in the remaining pool of market participants to set prices. I extended the argument to include the impact on retail investors, who, in being persuaded to take on equity market exposures through passive vehicles, rather than by picking individual stocks or active fund managers themselves, were rendered less likely to inject their own lack of skill into the market’s relative pricing mechanism. Granted, they will be just as likely to distort the market’s absolute valuation through their knee-jerk inflows and outflows into the market as a whole, but at least they will not be exerting additional influences on the market’s relative valuation, where their lack of skill would end up producing additional distortions.

Now, if market participants were to shift to a passive approach in the practice of asset allocation more broadly–that is, if they were to resolve to hold cash, fixed income, and equity from around the globe in relative proportion to the total supplies outstanding–then we would expect to see a similarly positive impact on the market’s absolute pricing mechanism, particularly as unskilled participants choose to take passive approaches with respect to those asset classes in lieu of attempts to “time” them. But, to be clear, a broader shift to that broader kind of passivity is not currently ongoing. The only areas where “passive” approaches are increasing in popularity are areas inside specific asset classes–specifically, inside the equity and fixed income markets of the developed world.

Active to Passive: The Emergence of Distortion

Passive investing may improve the market’s efficiency at various incremental phases of the transition, but there are limits to the improvement. To appreciate those limits, let’s assume that the migration from active to passive in our hypothetical market continues over the long-term, and that the number of active funds in the system ends up shrinking down to a tiny fraction of its initial size. Whereas the active segment of the market initially consisted of 999 active funds collectively controlling roughly 50% of equity assets, let’s assume that the active segment shrinks down to only 10 funds collectively controlling 0.5% of equity assets. The other 99.5% of the market migrates into the passive fund.

In evaluating the impact of this shift, it’s important to remember that active investors are the entities that set prices in a market. Passive investors cannot set prices, first because they do not have any fundamental notion of the correct prices to set, and second because their transactions are forced to occur immediately in order to preserve the passivity of their allocations–they cannot simply lay out desired bids and asks and wait indefinitely for the right prices to come, because the right prices may never come. To lay out a desired bid and ask, and then wait, is to speculate on the future price, and passive funds don’t do that. They take whatever price is there.

In the above configuration, then, the tiny segment of the market that remains active–which holds roughly 0.5% of the total equity supply–will have to set prices for all 5,000 securities in the market. It follows that a much smaller pool of resources will be devoted to doing the “work”–i.e., the fundamental research, the due-diligence, etc.–necessary to set prices correctly. For that reason, we should expect the configuration to substantially reduce the market’s efficiency, contrary to what I asserted earlier.

In our hypothetical market, a 1% active management fee was initially being levied on 50% of the market’s capitalization, with the proceeds used to fund the cost of due-diligence. After the migration, that 1% fee will be levied on only 0.5% of the market’s capitalization, yielding roughly 1/100 of the proceeds. The shrunken proceeds will have to pay for the cost of due-diligence on a security universe that hasn’t shrunken at all. Because the active segment will have a much smaller amount of money to spend on the due-diligence process, a new investor that enters and spends a given amount of money on it in competition with the active segment will be more likely to gain an edge over it. At the margin, active investors that enter at the margin will be more capable of beating the market, which is precisely what it means for the market to be less efficient.

This thinking is headed in the right direction, but there’s a subtle problem with it. The best way to see that problem is to trace out the literal process by which the active segment will end up shrinking. Suppose we return to where we initially started, with 999 active funds and 1 passive funds. In their efforts to arbitrage the 1% differential in expected returns, investors transfer large sums of money out of the 100 active funds with the worst performance track records, and into the market-performing passive fund, forcing the 100 active funds to shut down.

The 100 active funds that end up shutting down will have to sell their shares to raise cash to redeem their investors. But who will they sell their shares to? They might be able to sell some of their shares to the passive fund, because it will be receiving cash inflows, and will need to buy shares. But they won’t be able to sell all of their shares to the passive fund, because the passive fund will have to buy shares of every company in the market–all 5,000, in proportion to the supply oustanding–many of which the active funds won’t be holding. The passive funds will therefore have no choice but to buy at least some of their shares from the other 899 active funds that remain.

Working out the implications of the flows, then, the 100 underperforming active funds, in liquidating themselves, will have to sell at least some of their shares to the 899 remaining active funds. Those remaining active funds will be in a position to buy the shares, because they will have received cash from selling some of their own shares to the passive fund when it went in to buy. But before the remaining active funds can buy the new shares, they will have to conduct research–due-diligence–to determine the appropriate prices. That due-diligence will cost money. Where will the money come from?

Unfortunately, there is nowhere for it to come from, because the assets that the remaining active funds will have under management, and therefore the fee revenues that they will be able to earn, will not have increased. Crucially, in the migration, assets will not be moving from the 100 underperforming active funds to the remaining active funds who will perform the needed fundamental research on the shares being sold–rather, assets will be moving from the 100 underperforming funds to the cheapskate passive fund, which doesn’t spend any money at all on the research process, opting to simply give the money back to its investors instead. Consequently, the money needed to fund the additional research will not be available. Unless the money is taken out of some other necessary research activity, or out of the active fund manager’s wages or profits, the research and due-diligence necessary to buy the shares will not get done.

The following two schematics distinguish two types of migrations: a sustainable migration from active fund to active fund, and an unsustainable migration from active fund to passive fund.

In our scenario, the remaining active funds will not have done the research necessary to buy the shares that the underperforming funds will need to sell, and will not get paid any additional money to do that research. Consequently, they aren’t going to be interested in buying the shares. But the 100 underperforming active funds have to sell the shares–they have to get cash to redeem their investors. So what will happen? The answer: the bid-ask spread will effectively widen. Prices will be found at which the remaining active funds will be willing to transact–those prices will simply be much lower, to ensure adequate protection for the funds, given that they haven’t done the work necessary to be comfortable with the purchases, or alternatively, given that they need to pay for that work, and that the money has to come from somewhere.

The point articulated here is admittedly cumbersome, and it might seem out of place to think about the process in terms of the need to pay for “research.” But the point is entirely accurate. The best way to grasp it is to start from the endgame scenario that we posited, a scenario where active funds shrink down to some absurdly small size–say, 0.5% of the market, with the other 99.5% of the market invested passively. How do you get to a situation where a measly 0.5% of the market, a tiny group of managers that are only able to draw in a tiny revenue stream out of which to pay for fundamental research, is setting prices–placing bids and asks–on a massive equity universe consisting of 5,000 complicated securities? The only way you get there is by having bid-ask spreads completely blow out. If their counterparties are desperate, then yes, the tiny group of active funds will trade in securities that they aren’t familiar with or interested in, and that they haven’t done adequate due-diligence on. But they will only do so at prices that are sufficient to provide them with extreme margins of safety: ultra-low bids if they have to be the buyers, and ultra-high asks if they have to be the sellers.

In the previous piece on Indexville, we posed the question: what will happen if the active segment of the market becomes too small, or if it goes away completely? Most people think the answer is that the market will become “inefficient”, priced incorrectly relative to fundamentals, making it easier for new active investors to enter the fray and outperform. But we saw that that’s not exactly the right answer. The right answer is that the market will become illiquid. The bid-ask spread will blow out or disappear entirely, making it increasingly costly, or even impossible, for investors–whether passive or active–to transact in the ways that they want to.

The example above takes us to that same conclusion by a different path. If an active segment with a tiny asset base and tiny fee revenues is left to set prices on a large universe of complicated securities, the bid-ask spreads necessary to get that segment to transact will explode, particularly in those securities that it has not done sufficient research on and that it is not familiar with or comfortable transacting in–which will be most securities, given that a tiny segment of a large market cannot single-handedly do the work of studying and forming a sound fundamental opinion on everything inside it.

Liquidity Provision: A Way to Earn the Fees

We return to the question at the title of the previous section: Can the fees that active managers collectively charge be earned? The answer is yes. The fees can be earned out of revenues generated through the provision of liquidity–selling at the ask to those that need to buy, and buying at the bid from those that need to sell. The excess return over the market equals half the spread between the two, times the volume, divided by the capital employed. As the active segment of the market shrinks in size, that excess return will increase. At the same time, the fees extracted by the segment will decrease, bringing the segment closer to a condition in which its fees match its excess returns, which is what it means for the active segment to earn its fees.

The active segment of the market has two external counterparties that it can provide liquidity to: first, the passive segment, which experiences inflows and outflows that it must deploy and redeem, and second, the corporate sector, which sometimes needs to raise equity funding, and which, more frequently in the present era, wants to buy back its own shares. The total flows of those external counterparties–the total amount of buying and selling that they engage in–will determine the amount of excess return that the active segment can generate in providing liquidity to them, and therefore the maximum fees that it can collectively “earn.” Any fees that get extracted above that amount will be uncompensated for, taken from investors in exchange for nothing.

If the market were suffering from an inadequate amount of active management, the consequences would become evident in the performance of passive funds. Passive funds would begin to exhibit increased tracking errors relative to their benchmarks. Every time they received a cash inflow and attempted to buy shares, they would be forced to buy at the elevated ask prices set by the small number of active funds willing and able to transact with them, ask prices that they would push up through their attempted buying. Conversely, every time they received redemption requests and attempted to sell shares, they would be forced to sell at the depressed bid prices set by the small number of active funds willing to transact with them, bid prices that they would pull down through their attempted selling. On each round-trip, each buy followed by a sell, they would lodge a tracking loss relative to their indices, the mirror image of which would be the excess profit earned by the active segment in providing them with liquidity.

Now, you might think that liquidity in the market is already provided by specialized market-makers–e.g., computers trading on HFT algorithms–and that active, fundamentally-informed investors are not needed. But market-makers of that type only provide one small phase of the market’s liquidity–the phase that entails bridging together, over the very short-term, the temporarily divergent flows of participants that are seeking to hold shares for longer periods of time. Active investors, those that are willing to adjust their demand for shares based on fundamental value, are crucial to the rest of the process, because they are the only entities that are capable of buffering and balancing out longer-term flow imbalances that otherwise emerge in the market–situations, for example, where there is an excess of interested sellers, but no interested buyers, either present or en route, even after the ask price is substantially lowered. Without the participation of value-responsive active investors in those situations, market-makers would have no buyers to bridge the selling flows against, and would therefore have to widen their spreads, i.e., lower their bids–or even remove them from the market altogether.

Right now, the average tracking error in the average passive fund is imperceptible. This fact is proof that the current market, in its ongoing migration into passive funds, isn’t even close to suffering from an insufficiency of active management. With at most 40% of the equity market having gone passive, the point in the transition where tangible market illiquidity will ensue is still very far away.

That’s why, in the previous piece, I argued that the active segment of the market is not even close to being able to earn its fees in the aggregate. Active managers aren’t doing anything wrong per se, it’s just that the shrinkage they’ve suffered hasn’t yet been extreme enough to undermine the function they provide, or make the provision of that function profitable enough to reimburse the fees charged in providing it. Granted, they may be able to earn their fees by exploiting “dumb-money” categories that we haven’t modeled in our hypothetical market–e.g., retail investors that choose to conduct uninformed speculation in individual shares, and that leave coins on the floor for skilled managers to pick up behind them–but they aren’t even close to being able to collectively earn their fees via the liquidity they provide to the other segments of the market, which, evidently, are doing just fine.

The Actual Forces Sustaining Active Management

Active managers, in correctly setting prices in the market, provide a necessary benefit to the economy. In a mature, developed economy like ours, where the need for corporate investment is low, and where the corporate sector is able to finance that need out of its own internal cash flows, the benefit tends to be small. But it’s still a benefit, a contribution that a society should have to pay for.

Right now, the people that are paying for the benefit are the people that, for whatever reason, choose to invest in the active segment of the market, the segment that does the work necessary to set prices correctly, and that charges a fee for that work. But why do investors do that? Why do they invest in the active segment of the market, when they know that doing so will leave them with a lower return on average, in exchange for nothing?

The question would be more apt if active investors were investing in a fund that owned shares of all actively-managed funds–an aggregate fund-of-all-active-funds, if one can envision such a monstrosity. Investors in such a fund would be giving away the cost of fees in exchange for literally nothing—a return that would otherwise be absolutely identical to the passive alternative in every conceivable respect, except for the useless drag of the fees.

But that is not what people that invest in the active segment of the market are actually doing. Active management is not a group sport; the investors that invest in it are not investing in the “group.” Rather, they are investing in the individual active managers that they themselves have determined to be uniquely skilled. It’s true that they pay a fee to do that, but in exchange for that fee, they get the possibility of outperformance–a possibility that they evidently consider to be likely.

Every investor that rationally chooses to invest in the active segment of the market makes the choice on that basis–an expectation of outperformance driven by the apparent skill of the individual active manager that the investor has picked out. Whereas this choice can make sense in individual cases, it cannot make sense in the average case, because the average of the group will always be just that–average in performance, i.e., not worth extra fees. In choosing to invest in the active segment, then, active investors are choosing, as a group, to be the gracious individuals that pay for the cost of having “correct market prices”, in exchange for nothing. Passive investors are then able to free-ride on that gracious gift.

How, then, is the active segment of the market able to remain so large, particularly in an environment where the fees charged are so high, so much more than the actual cost of doing the fundamental research necessary to have a well-functioning market? Why don’t more active investors instead choose the passive option, which would allow them to avoid paying the costs of having a well-functioning market, and which would net them a higher average return in the final analysis?

The answer, in my view, is two-fold:

(1) The Powers of Persuasion and Inertia: For every active manager, there will always be some group of investors somewhere that will be persuaded by her argument that she has skill, and that will be eager to invest with her on the promise of a higher return, even though it is strictly impossible for the aggregate group of managers engaged in that persuasive effort to actually fulfill the promise. Moreover, absent a strong impetus, many investors will tend to stay where they are, invested in whatever they’ve been invested in–including in active funds that have failed to deliver on that promise.

(Side note: Did you notice how powerful that shift from the use of “he” to the use of “she” was in the first sentence of the paragraph above? The idea that the manager that we are talking about here is a female feels “off.” Moreover, the connotation of deceipt and trickery associated with what the active manager is doing in attempting to convince clients that he has special financial talents and that his fund is going to reliably outperform is significantly reduced by imagining the manager as a female. That’s evidence of ingrained sexual bias, in both directions).

(2) The Framing Power of Fee Extraction: Fees in the industry get neglected because they are extracted in a psychologically gentle way. Rather than being charged as a raw monetary amount, they are charged as a percentage of the amount invested. Additionally, rather than being charged abruptly, in a shocking one-time individual payment, they are taken out gradually, when no one is looking, in teensy-weensy daily increments. As a result, an investor will end up framing the $10,000 fee she might pay on her $1,000,000 investment not as a literal payment of $10,000 that comes directly out of her own pocket, but rather as a negligible skim-off-the-top of a much larger sum of money, taken out when no one is looking, in miniscule incremental shavings that only accumulate to 1% over the course of a full year.

To illustrate the power that this shift in framing has, imagine what would happen if the DOL, in a follow-up to its recent fiduciary interventions, were to require all annual fees to be paid at the end of each year, by a separate check, paid out of a separate account. Then, instead of having the 1% fee on your $1,000,000 mutual fund investment quietly extracted in imperceptible increments each day, you would have to cut a $10,000 check at the end of each year–go through the process of writing it out, and handing it over to the manager, in exchange for whatever service he provided. $10,000 is a lot of money to pay to someone that fails to deliver–even for you, a millionaire!

If the way fees are framed were forcibly modified in this way, investors would become extremely averse to paying them. The ongoing shrinkage of the market’s active segment–in both its size and its fees–would accelerate dramatically. The effects of the policy might even be so powerful as to push the market into a state in which an acute scarcity of active management ensues–a situation in which everyone attempts to free-ride on the index, and no one steps up to pay the expenses associated with having a well-functioning market. If that were to happen, active funds would find themselves capable of generating excess returns from the provision of liquidity that substantially exceed the fees they charge. Investors in active funds, who are the only ones actually paying the cost of that service, would begin to receive a benefit for having paid it, a benefit that would be well-deserved.

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The growing popularity of passive investing provokes a series of tough questions:

What necessary functions does active management perform in a financial system?

What is the optimal amount of active management to have in such a system, to ensure that those functions are carried out?

If the size of the market’s active share falls below the optimal level, how will we know?

How much can active managers, as a group, reasonably charge for their services, without acting as a net drag on the system?

To answer these questions, I’m going to explore the curious case of Indexville, an economy whose investment sector has been designed to be 100% passive. As expected, Indexville lacks a number of features that are necessary for the optimal functioning of an economy. I’m going to try to build those features back into it, documenting the cost of doing so each step of the way. Ultimately, I’m going to run into a problem that ingenuity cannot overcome. That problem is the exact problem that active management is needed to solve.

A Journey Into Indexville

Indexville is an economy similar in its composition to the United States economy, with one glaring exception: the citizens of Indexville consider active management to be unproductive and immoral, and are therefore invested in Indexville’s corporate sector 100% passively, through a fund called INDX. The system works as follows:

When the citizens of Indexville earn excess cash, they have two options:

(1) Hold it in the bank, where it will earn a small interest rate set by the government–an interest rate of, say, 1% real.

(2) Purchase new shares of the economy’s sole investment vehicle, an index mutual fund called INDX.

When INDX sells new shares to investors, it invests the proceeds in one of four private equity funds–PVT1, PVT2, PVT3, and PVT4. These private equity funds, which are independently operated, compete with each other to provide equity financing to the corporate sector. The financing can take the form of either an initial investment, in which a new company is created, or a follow-on investment, in which an existing company is given additional funds for expansion.

If we wanted to, we could broaden the scope of the funds, allowing them to make debt investments in addition to equity investments, not only in the corporate sector, but in the household and government sectors as well. But we want to keep things simple, so we’re going to assume the following:

All private sector investments in Indexville are made through the corporate sector, and the financing is always through equity issuance. There are no homeowners in Indexville, for example–everyone in Indexville rents out homes and apartments from corporations that own them.

Direct investment in Indexville’s government sector is not possible. All federal, state and local Indexville paper is owned by the banking system, which is where the small amount of interest paid to cash depositors ultimately originates. If investors want a risk-free option, they already have one: hold cash.

For now, we assume that buying INDX shares is a one way transaction. The shares cannot be redeemed or sold after purchase. Redeeming them would require de-capitalizing the corporate sector, which is unrealistic. Trading them with other people is possible, but the option has been made illegal, consistent with Indexville’s moral ethos of total investment passivity: “Thou shalt not trade.”

Now, every existing company in Indexville was created through the above investment process, so INDX owns the entire corporate sector. That’s what allows us to say that all INDX investors are invested “passively” relative to that sector. Recall the definition we proposed for a passive allocation:

Passive Allocation: A passive allocation with respect to a given universe of assets is an allocation that holds every asset in that universe in relative proportion to the the total quantity of the asset in existence.

The total quantity of corporate assets in Indexville literally is INDX. Whatever the relative proportion between the quantities of the different assets inside INDX happens to be, every investor will own them in that relative proportion, simply by owning INDX shares.

Now, to be fair, the investors in INDX are not passively allocated relative to the entire universe of Indexville’s financial assets, which includes both equity and cash. Though such an allocation might be possible to achieve, it would clearly be impossible to maintain in practice. Anytime anyone spent any money, the spender would decrease his cash, and the recipient would increase it, throwing off any previously passive allocation that might have existed.

The word “passive” can take on another important sense in these discussions, which is the sense associated with a “passive ethos”, where investors refrain from placing trades for speculative reasons, and instead only trade as necessary to carry out their saving and consumption plans, or to transition their portfolios to a state that matches their risk tolerances as they age. This is the sense of the term found in the advice of the gurus of “passive” investing–Jack Bogle, Burton Malkiel, Eugene Fama, and so on. Indexville investors follow that advice, and fully embrace a “passive ethos.”

Returning to the structure of Indexville, the excess profits of the individual companies in Indexville are periodically distributed back up to their respective private equity funds as dividends, and then back up to INDX, and then back up to the investors. These dividends represent the fundamental source of INDX investor returns. Without the potential to receive them, shares of INDX would be intrinsically worthless.

Instead of relying on equity issuance, corporations in Indexville have the option of funding new investment out of their own profits. When they choose to do that, they reduce the dividends that they are able to pay to the private equity funds, which in turn reduces the dividends that the private equity funds are able to pay to INDX investors. But the reduction is compensated for in the long-term, because the new investment produces real growth in future profits, which leads to real growth in future dividends paid.

Cost #1: Conducting Due-Diligence on New Investment Opportunities

To make sound investments–whether in new companies seeking initial capital, or in existing companies seeking follow-on capital–the private equity funds have to conduct appropriate due-diligence on candidate investment opportunities. That due diligence requires research, which costs money–the funds have to hire smart people to go and do it.

Where will the money to pay these people come from? Unfortunately, Indexville’s passive structure has no magic bullet to offer here–the money will have to come from the only place that it can come from: out of investor returns, as fees. It will get subtracted from the dividends paid to the private equity funds, and therefore from the dividends paid to INDX, and therefore from the dividends paid to investors.

What we’ve identified, then, is the first unavoidable cost of a 100% passive system:

Cost #1: The need to pay people to conduct appropriate due-diligence on new investment opportunities, so as to ensure that INDX investor capital is allocated productively and profitably, at the best possible price.

Note that Cost #1 is not driven by a need to put a “trading” price on already-existing companies. The trading prices of such companies do not matter to INDX investors, since INDX already fully owns them, and has no one to sell them to but itself. Nor do the prices matter to the economy, because the physical capital that underlies them has already been formed. The price that people decide to trade that capital at does not affect its underlying productivity.

The need that gives rise to Cost #1 is the need to determine whether a company is an appropriate target for new investment–taking new investor funds, new economic resources, and putting them into a startup, or a struggling company–and whether the investment will produce a better return than other available opportunities, given the proposed price. Mistakes made in that determination have a direct negative impact on investor performance, and lead to suboptimal allocation of the economy’s labor and capital resources.

Let’s ask: what is a reasonable estimate of the total expense associated with Cost #1? How much should we expect it to detract from INDX’s returns? The answer will depend on how much new investment the private equity funds engage in. Recall that most of the investment in Indexville will be carried out by already-existing companies, using retained profits as the funding source. The cost of the research done in association with that investment is already reflected in the net profits of the companies.

The U.S. has roughly 5,000 publicly-traded companies. To be conservative, let’s assume that Indexville’s corporate sector is similarly sized, and that 1,000 companies–20% of the total–seek new funding each year, either in initial public offerings or, more commonly, in follow-on offerings. We want Indexville’s capital to be allocated as productively as possible, so we assign two extremely talented analysts to each company, at an annual cost of $300,000–$200,000 in salary, and $100,000 in capital investment to support the research process. For a full year, the analysts spend the entirety of every workday researching their assigned individual company, rigorously weighing the investment opportunity. The resulting cost:

1000 * 2* $300,000 = $600,000,000.

The U.S. equity market is valued at roughly $30T. Expressed as a percentage of that overall total, the annual cost of investment due diligence in Indexville amounts to 0.002% of total assets.

Of course, we want to have the benefits of aggressive competition in Indexville. So we multiply that cost by 4, to reflect the fact that each of the four funds will carry out the research program independently, in competition with each other. To be clear, then, the four funds will each have 2,000 analysts–8,000 in total–who each spend an entire year effectively researching one-half of a single investment opportunity, at a cost of $300,000 per analyst per year. The total annual expense: 0.008% of total marketable assets.

Consistent with Indexville’s emphasis on engineered competition, an advisory board for INDX has been created. Its responsibility is to evaluate the long-term investment performances of the four private equity funds, and adjust the amount of future funding provided to them accordingly. Funds that have made good investments get a larger share of the future investment pie, funds that have made bad investments get a smaller share. Similar adjustments are made to manager pay. Managers of strongly performing funds see their pay increased, managers of poorly performing funds see their pay decreased.

What will the advisory board cost? Assuming 50 people on it, at an annual cost of $500,000 per person, we get $25MM, which is 0.00008% of assets–in other words, nothing.

Cost #2: Determining a Correct Price for INDX Shares

When investors buy new shares in INDX, they have to buy at a price. How is that price determined? Recall that Indexville’s corporate sector is entirely private. There is no market for the individual companies. Nor is there a market for INDX shares. It follows that the only way to value INDX shares is to calculate the value of each underlying company, one by one, summing the results together to get the total. That’s going to cost money.

So we arrive at the second unavoidable cost of a 100% passive system:

Cost #2: The need to pay people to determine the values of the individual companies in the index, so that new shares of the index can be sold to investors at fair prices.

Cost #1 was a worthwhile cost. The underlying work it entailed was worth doing in order to maximize INDX shareholder returns and ensure efficient capital allocation in Indexville’s economy. Cost #2, in contrast, is a net drag on the system. It has no offsetting benefit, and can be avoided if the participants embrace a cooperative mentality.

Suppose that a mistake is made in the calculation of INDX’s price, and an investor ends up paying slightly more for INDX shares than he should have paid. The investor will see a slight reduction in his returns. That reduction, of course, will occur alongside a slight increase in the returns of existing investors, who will have taken in funds at a premium. In the end, the aggregate impact on the returns of the system will be zero, because price-setting is a zero-sum game.

Now, the direct, short-term impact of pricing mistakes may be zero-sum, but the long-term effect can be negative, particularly if the mistakes cause people to alter their future behaviors in undesirable ways. If consistent inaccuracies are tolerated, people might try to find ways to “game” them. They might also become disgruntled, and cease to participate in the investment process. If that’s what’s going to happen, then we’re not going to have much of a choice: we’re going to have to spend the money needed to make sure the price is as right as it can be, for every new share sale, every day. The cost will come out of everyone’s return, reflecting the drag on the system brought about by the non-cooperative mentality.

Given that Indexville’s corporate sector is roughly the same size as the public market of the United States, the task of accurately calculating the fund’s price will entail valuing roughly 5,000 individual companies. The proposed plan is as follows. As before, we hire two highly talented analysts for each company. We give each analyst the singular responsibility of building a valuation estimate for the company, and adjusting the estimate on a daily basis to reflect any new information that becomes available. The basic instruction to each analyst is:

Develop an estimate of the company’s future cash flows, and discount those cash flows at a required real rate of 6%, which is what Indexville investors consider to be a fair return. Focus on getting the cash flows right. Your pay will be tied to how well you do that.

Where there is uncertainty, identify the different possibilities, and weigh them by their probabilities. Do not let the desire to be right in your past analysis influence your future analysis–instead, respond to the facts as they present themselves, with a singular focus on truth, i.e., “what is actually going to happen?”, rather than “what do I personallywant to happen?” If necessary, examine past valuation work done on similar companies, especially work done by top-performing analysts, and use their insights to help you triangulate towards a reasonable number.

Try to be consistent. Don’t dramatically change your valuation estimates from day to day unless something relevant and impactful has taken place–e.g., the company has released an earnings report with important new information in it.

To get to a price for the INDX, we take the two valuation estimates produced for each company and average them together. We then sum the resulting averages, arriving at a total market capitalization for the fund. We then divide the fund’s market capitalization by its number of shares, arriving at a final price. That price is the price at which we sell new shares to investors, with the sales, occurring each day, at the end of the day.

How much will this project cost annually?

5,000 * 2 * $300,000 = $3,000,000,000

But let’s assume that we really want to get the final numbers right, to ensure fairness for all Indexville investors. So we double the effort. We put four analysts on every company, instead of two. The result:

5,000 * 4 * $300,000 = $6,000,000,000

So, $6,000,000,000. Relative to the (assumed) total market capitalization of Indexville’s universe of companies, $30T, the cost represents 0.02% of assets.

Now, you might think that an actual market’s estimate of corporate value will be more accurate than the estimates of these 20,000 analysts. But you have no evidence of that. What would evidence even look like? Markets don’t publish their “future cash flow estimates”, nor do they reveal their “discount rates.” These artifacts can only be arrived at tautologically, by extracting them together from the price. And either way, it doesn’t matter. As long as the citizen’s of Indexville believe that the estimates of the 20,000 analysts are accurate, and maintain their trust in the system, actual inaccuracies will not affect anything, because price-setting, again, is a zero-sum game.

Cost #3: The Provision of Liquidity

Up to this point, we’ve identified two costs that investors in Indexville will have to bear, given that they don’t enjoy the benefits of active management.

The first was the cost of conducting due-diligence on new investment opportunties. Actual cost: 0.008% of assets.

The second was the cost of valuing existing companies in the fund so as to determine a fair sale price for new shares. Actual cost: 0.02% of assets.

Both costs proved to be extremely small. Clearly, then, a large active segment is not needed to solve them, especially not at typical active fee levels, which can be anywhere from 25 to 100 times higher.

Unfortunately, there’s a huge problem with Indexville’s system that we haven’t addressed: the problem of liquidity. An investor can convert cash into INDX by purchasing shares, but what if an investor wants to go the other way, and convert INDX shares back into cash? In its current configuration, Indexville doesn’t offer the option to do that.

Unlike money, or even a debt security, an equity security is intrinsically illiquid. It has no maturity date, and offers no direct method of redemption. The cash that went into purchasing it is effectively gone. The only way to directly get that cash back is to have the corporate sector liquidate–a solution that is not realistically possible, and that would require investors to take losses if it were.

What is the real cost of the illiquidity of an equity security? Answer: the inconvenience imposed on the owner. The owner has to factor the cost of the illiquidity into his pricing of the security. If he is making an investment in a new company, and is taking a full equity stake in it, he will have to require a higher future return–higher not to make the overall deal any better for him, but simply to compensate him for the significant drawback associated with losing his ability to access his money. The higher return hurdle that he will be forced to place on the process will disqualify investment prospects that would otherwise be beneficial to everyone, if they were liquid. Similarly, if he is making an investment in an existing company owned by someone else, he is going to have to demand a lower price for his stake. That lower price will come at the existing owner’s expense, rendering the issuance less attractive to the existing owner, and causing him to not want to take in funds and make investments that would otherwise be beneficial to everyone, if liquidity existed.

The cost of illiquidity is real, and therefore it’s important that we find a way to make INDX liquid. So here’s a simple proposal: we give investors an option to sell–not to other people, but to INDX directly, in a mutual fund redemption process. Every day, at the end of the day, we pair buyers and sellers of the fund, exchanging the incoming cash and the existing shares between them. If you are seeking to buy, I pair you with a seller. You take his shares, he takes your cash. And vice-versa. This won’t cost us anything extra, because we already know the fair value of the fund from the prior calculations that we paid for. Investors will then have liquidity.

Indexville’s citizens are likely to be averse to this suggestion, because it enables the toxic practice of market timing. But there are legitimate, non-speculative reasons why an investor may want to sell shares. For example, the investor may be entering a later of phase of her life, and may want to withdraw the funds to spend them down. Either that, or she may simply prefer a more liquid allocation, and be willing to give up some return in exchange for it. Some other investor may have similarly legitimate reasons for wanting to buy new shares–the investor might be in a younger phase of life, and have a greater need to save, or want more growth. What is the harm in pairing the two together, exchanging the shares and cash between them? The exchange may be zero-sum in terms of how the future returns get divided, but it will be positive sum in terms of its overall impact–both investors will end up winners. This contrasts with a scenario where the two investors trade for speculative reasons, because one thinks the price is going to rise, and the other thinks the price is going to fall. That trade will be zero-sum. One trader is going to be right, and the other trader is going to be equally wrong.

Let’s assume that we’re able to convince the citizens of Indexville that there are legitimate uses for liquidity, and that everyone will ultimately benefit from the introduction of a sale option in INDX shares. We’re still going to run into a problem. How will the fund deal with periods in which there is more buying than selling, or more selling than buying? In those periods, excess buyers and sellers will end up leftover, with orders that cannot be met. What will the fund do with them?

If there is more buying than selling, the fund can always issue new shares. But the private equity firms may not need new funds. There may not be any attractive investment opportunities–with returns of 6% or better–for them to deploy the funds into. If we allow new shares to be created at 6%, when there are no 6%-or-better investments for the funds to invest in, we will be harming existing shareholders, diluting their stakes in exchange for nothing.

If there is more selling than buying, the situation becomes more complicated. One option is to take the cash dividends of other investors, and give those dividends to the sellers, in exchange for their stake. On this option, the existing investors will effectively be “reinvesting” their dividends. But they may not want to do that. And even if they do want to do it, the dividend payments in a given quarter may not be enough to fully meet the selling demand. Another option would be for INDX to borrow cash to pay exiting shareholders. On this option, the remaining investors will essentially be levering up their stakes. Again, they may not want to do that. And even if they do want to do it, the option of borrowing for that purpose may not be something that the banking system in Indexville is willing to make available.

Apart from forced dividend reinvestment and forced leveraging, the only other way for INDX to get the cash needed to pay the exiting investors would be to have the corporate sector liquidate, i.e., sell itself. But, again, assuming that all of the capital that went into the funds and companies has been deployed, who exactly are the companies going to sell themselves to? INDX is the only possible buyer, and it has no cash. It’s trying to get cash, to redeem the investors that want to sell it.

A final option would be for INDX to change its price. Instead of having investors exchange shares at a price associated with an implied rate of return of 6%, it could raise or lower the price–i.e., decrease or increase the implied rate of return–in order to discourage buying or selling and balance the demand. Unfortunately, that won’t work. Indexville’s investors are entirely passive. They make investment decisions based on their personal savings and consumption needs, not based on valuation arbitrage, which they do not understand. INDX can raise its price to infinity, or drop its prize to zero–either way, the buying and selling demand of the system will not change. The only thing that will change is that certain unlucky people will end up getting screwed–denied the “fair value” return that they deserve, 6%.

With the above options ruled out, INDX’s only remaining option will be to simply say no:

“We’ve received your sale order. Due to market conditions, we are not currently able to execute it. However, we’ve placed your name in a queue. Currently, you are number 47 in the queue, with $400MM worth of selling demand in front of you. Once we’ve found buyers to take on that selling demand, any subsequent buy orders will be routed through you.”

The problem with this option, of course, is that it represents a loss of investor liquidity. Investors will only have guaranteed immediate liquidity if they are lucky enough to be going against the prevailing investment flows. Otherwise, they will have to wait.

But would that really create a problem? It would certainly create a problem if Indexville’s investors were inclined to trade for speculative reasons. The mere perception of impending excess buying or selling demand would incent them to buy or sell, reflexively exacerbating the ensuing flow imbalance. But Indexville’s investors are not like that. Consistent with Indexville’s passive ethos, they only make trades for legitimate personal reasons–because they have savings to invest, or because they need to draw down on their savings in order to fund their lifestyles.

In certain situations where a large imbalance naturally develops in the economy’s saving preferences, the answer is, yes, it would create a problem. One can imagine, for example, a scenario in which the average age of Indexville’s citizenry increases dramatically, resulting in a large population of older people with a preference for redeeming shares, and only a small population of younger people with a preference for purchasing them. In such a scenario, the older generation will lose its liquidity. But as long as Indexville’s economy remains capable of producing what its citizens want and need, any ensuing problem will be illusory–a problem that results entirely from the accounting artifacts–“shares”, “cash”, etc.–that are being used to divide up the economy’s purchasing power. Policy intervention could easily solve it–for example, by having the government print cash and purchase the shares from the older generation at fair value.

Now, everything I’ve just said is based on the assumption that Indexville’s investors are fully passive, that they do not respond to valuation arbitrage. If that’s not true, i.e., if they have even the slightest of speculative instincts, then the problems with the above proposal will compound. Assuming that Indexville’s economic condition is similar to the current economic condition of the United States, the discount rate at which prices for the fund have been set, 6%, will be too high relative to the small interest rate, 1%, that can be earned on the alternative, cash. The economy will not have a sufficient quantity of investment opportunities, with returns of 6% or better, in order to meet that saving demand. INDX will therefore see a persistent excess of buying–especially if the buyers are reflexively aware that the economy’s strong saving demand will guarantee them future liquidity, should they ever want to sell.

But if Indexville’s investors are active, and respond to valuation arbitrage, then a previously discarded solution will work just fine. All that INDX will have to do to balance the flows is change the price at which purchase and sale orders are executed. If there is too much buying demand, raise the price–the lower implied return will lead to a reduction in buying demand. If there is too little buying demand, lower the price–the higher implied return will increase the buying demand. Of course, to embrace this solution, Indexville’s investors are going to have to abandon the notion that anything other than a 6% return is “unfair.” If there is strong demand for saving in the economy, and if the private equity funds cannot find sufficient investment opportunities with a return above 6% to deploy that saving into, then lower returns will simply have to be accepted.

In the above case, there are tools that the government can use to create higher returns for investors. But those tools come with separate costs. It doesn’t make sense for the society to offer to bear those costs simply to improve the average investor’s lot. The right answer is for investors to accept lower rates of return, which is fair compensation for their investment contributions, given the economy’s reduced need for them.

Returning to the assumption that Indexville’s investors are completely passive and insensitive to arbitrage, there will be no way to address flow imbalances other than by make people wait their turn. The cost of that approach is lost liquidity.

Cost #3: the cost of providing liquidity in situations where the legitimately passive buying and selling flows going into and out of the index fail to balance out.

Unfortunately, there is no amount of money that Indexville can spend to cover that cost, i.e., to provide the desired liquidity. For Indexville to have it, some investor somewhere will have to agree to go active.

Market-Making and Active Management

When you place an order in the market to buy a share of stock, how do you place it? If you’re like most people, you place it either as a market order, or as a limit order above the lowest ask price. You do that because you want the order to execute. You want to buy now. If you thought that a better time to buy would come later, you would just wait.

Instead of insisting on buying now, why don’t you just put a limit order in to buy below the prevailing price, and go on about your business? Because you’re not stupid. To put in a limit order below the market price, and then walk away, would be to give the rest of the market a 100% free put option on the stock, at your expense. If the stock goes higher, the gains will end up going to someone else. If the stock goes lower, you will end up buying it, and will get stuck with the losses. Why would you agree to a let someone else have the gains on an investment, while you take the losses?

But wait. There was a limit order to sell that was just sitting there–specifically, the order that you intentionally placed your buy price above, so as to guarantee an execution. Where did that order come from? Who was the person that just stuck it in there, and walked away? What was his thinking?

The person who put that order in, of course, was the market-maker–the person who does the work necessary to create a liquid market. Market orders do not come into the system at the same time. Someone therefore has to bridge them together. That is what a market-maker does. When no one else is around, he puts a bid order in to buy at some price, and an ask order in to sell at some price, slightly higher. He then waits for those that want to trade now to come in and take his orders. In each round-trip transaction, each buy followed by a sell, he earns a spread, the spread between his bid and ask.

The following equation quantifies his revenue:

Revenue = 1/2 * Volume * Spread

So that is his revenue. What is his cost?

His first cost is the cost of doing the work necessary to find out where the right price for the market is. To ensure that he earns the spread, he has to identify the balancing point for the market, the general level at which the buying flow and the selling flow will roughly match. That is the level around which he has to place his orders, so that roughly the same number of people buy from him as sell to him. If he fails to target that level correctly–i.e., if he places his bid and ask orders at levels where the flows will become imbalanced–he will end up accumulating unwanted inventory.

His second cost is the cost of being wrong on the correct market price. If he is wrong, and ends up accumulating unwanted inventory, he will have to either hold that inventory indefinitely, or liquidate it, both of which will occur at a cost. To mitigate the impact of that cost, the market-maker will have to do at least a minimal amount of work to assess the value of what he is offering to hold. He has to know what it’s actually worth, in some fundamental sense, in case he gets stuck holding it.

For market-making to be profitable, the revenue earned has to exceed the costs. There will inevitably be risk involved–one can never be sure about where the balancing point in the market is, or about what the inventory being traded is actually worth from a long-term perspective, or about the magnitude of the losses that will have to be taken if it has to be liquidated. The associated risk is a risk to the market-maker’s capital. For market-making to be attractive, that risk requires a return, which ends up being the total round-trip volume times the spread minus the costs and the trading losses, divided by the amount of capital deployed in the operation.

What Indexville needs is for an active investor to step up and become a market-maker for INDX, so that temporary imbalances in the quantities of buyers and sellers can be smoothed out. The market-maker needs to figure out the patterns that define INDX transactions: When does there tend to be too much buying? When does there tend to be too much selling? If the market-maker can correctly answer those questions, he can bridge the excesses together, eliminating them through his trades. That is what it means to “provide liquidity.”

Given that Indexville’s investors are passive and unresponsive to arbitrage, a potential market-maker won’t even have to worry about what the right price point for INDX shares is. All that will matter is the future trajectory of the flow imbalances, which is entirely set by non-speculative preferences. If the market-maker can accurately anticipate that trajectory, he will be able to set the price wherever he wants, earning as much profit as he wants, without having to unbalance his own holdings.

Will Indexville’s investors get bilked in this arrangement? No. If the market-maker imposes an unreasonably high spread–only offering to buy shares, for example, at an 8% implied return, and only offering to sell them, for example, at a 4% implied return–then other potential active investors will take note of his outsized profits, and enter the fray to compete with him, becoming market-makers themselves. They will jump in front of his bids and asks, forcing him to either compress his spread, or let them get the executions. They will also force him to do more research, because they will now be there to arbitrage his mistakes. Ultimately, the revenue that he is able to earn, and that the Indexville investment community will have to pay him, will converge on his cost of doing business, which is the cost of studying and understanding the market, figuring out what the underlying securities are actually worth, and risking the possibility of getting stuck with someone else’s illiquidity.

Notice that these are the same costs that, up to now, Indexville has had to pay separately, given that it has no active investors. When active investors enter to make a market, the costs no longer need to be paid separately–the active investors can provide the associated services, with the rest of the market compensating them in the form of market-making profits.

Enter Warren Buffett

In February of this year, Druce Vertes of StreetEye wrote an exceptionally lucid and insightful piece on the topic of Active Management. In it, he asked the following question: what would happen if everyone in the market except Warren Buffett were to go passive? He showed, correctly, that Buffett could still beat the market.

In the scenario, when the passive segment of the market wants to sell, Buffett is the only potential buyer. Buffett is therefore able to demand a low price, a discount to fair value. When the passive segment wants to buy, Buffett is again the only potential seller. He is therefore able to demand a high price, a premium to fair value. On each go-round, each shift from passive net selling to passive net buying, Buffett buys significantly below fair value, and sells significantly above it, generating the superior returns that he is famous for.

What is Buffet doing in this example? He is earning the outsized revenues that inevitably come when you provide liquidity to a market that needs it. Those revenues easily cover the cost of providing that liquidity, which is the cost of understanding the psychology of the passive investors, so as to anticipate their net flows, and also the cost of determining the fair value of the underlying securities, to know what prices he can prudently pay for them, in case he gets stuck holding them.

What Indexville needs, then, is a Warren Buffett. But how profitable can Buffett really be in Indexville? The passive investors in Druce’s example appear to be dumb money investors that simply want to time the market, with Buffett as their counterparty. Buffett, of course, is easily able to smoke them. In Indexville, however, things aren’t going to be anywhere near as easy. The only flows that Buffett will have at his disposal will be the minimal flows associated with a passive ethos. Investors in Indexville buy in for one reason and one reason alone: because they have excess savings to invest. They sell out, again, for one reason and one reason alone: because they’re at a point in their lives where they need the funds. There is no speculation, no market timing, no giving away free money to Warren Buffett. The profits that Buffett will be able to earn will therefore drop significantly. And the economy as a whole will be better off for it, because a massive amount of zero-sum friction will have been removed, released for productive use elsewhere.

The Value of Active Management

In the previous two pieces, we expressed the Law of Conservation of Alpha, attributable to William Sharpe:

The Law of Conservation of Alpha: Before fees, the average performance of the investors that make up the active segment of a market will always equal the average performance of the investors that make up the passive segment.

This law does not apply to cases where we define “passive” in a way that allows the passive segment to trade with the active segment. To account for such cases, we need a new law:

The Law of Conservation of Alpha, *With Liquidity: Before fees, the average performance of the investors that make up the active segment of a market will exceed the average performance of the investors that make up the passive segment, by an amount equal to the market-making profits that the active segment earns in providing liquidity to the passive segment.

With this law in hand, we are now in a position to answer the four questions posed at the outset.

First, what necessary functions does active management perform in a financial system?

Answer: The function of providing liquidity to the market, specifically to the passive segment, and to companies seeking funding. In seeking to fulfill that function profitably, the active segment ends up providing the other functions of ensuring that new investment capital is correctly allocated and that existing assets get correctly priced, functions that Indexville had to pay for separately, because it lacked an active segment.

The provision of this liquidity obviously comes at a cost, the cost of doing the work necessary to know how the flows of the passive segment are likely to unfold, and also the work necessary to ascertain the underlying value of the existing securities being traded and the new investment opportunities being pursued.

Second, what is the optimal amount of active management to have in a financial system, to ensure that those functions are carried out?

Answer: The amount needed to ensure that adequate liquidity is provided to the market, specifically to the passive segment of the market and to companies seeking funding, assuming that the passive segment is not structured to provide that funding (as it was in Indexville). If there is adequate liquidity, prices will tend to be correct; if they are incorrect, those participants that are causing them to be incorrect will be exposed to arbitrage by other participants, which will render their liquidity provision unprofitable.

At this point it’s important to note that self-described “passive” investors are themselves the ones that determine how much active management will be needed. If the segment of the market that is proudly calling itself “passive” right now is only going to embrace “passivity” while things are good, morphing itself into an active, speculative, market-timing operation as soon as things turn sour, then a large number of active investors will be needed to come bail it out. As a group, those active investors will get the opportunity to earn their fees and outperform. But if investors come to their senses, and take a long view similar to the one embraced in Indexville, then the market’s liquidity needs will be minimal, and a market with a small active segment will be able to function just fine.

Third, if the size of the market’s active share falls below the optimal level, how will we know?

Answer: The market will show signs of not having enough liquidity.

If there is an insufficient amount of active management in the system, then whenever the passive segment introduces a net flow, prices will take on wild swings, and will become substantially disconnected from fair value. The problem, however, will be self-correcting, because there will then be a greater financial incentive for investors to go active and take advantage of the lucractive reward being offered for providing liquidity. The active segment as a whole will see stronger performance.

Fourth, how much can active managers, as a group, reasonably charge for their services, without acting as a net drag on the system?

Answer: An amount equal to the excess profit that they are able to earn in providing liquidity to the market, specifically to passive investors and companies seeking funding.

The active segment needs to earn its fees. If it can’t earn its fees, then there will always be an arbitrage opportunity putting pressure on its size. Investors will be able to get higher returns by going passive, and that’s what they’ll do.

The only way the active segment, as a group, can earn its fees, is by providing liquidity to the market, specifically to the passive segment, and to corporations seeking new funding. Of course, the active segment can trade with itself, attempting to arbitrage its own mistakes in that effort, but for every winner there will be a loser, and the net profit for the group will be nothing. Any fees charged in the ensuing cannibalization will represent a loss to investors relative to the alternative–which is to simply go passive.

In terms of the larger benefit to society, the cannibalization may cause prices to become more “correct”, but how “correct” do they need to be? And why does their “correctness” require such an enormous and expensive struggle? Recall that in Indexville we were able to buy a decent substitute for the struggle–a 20,000-person army of highly talented analysts valuing the market–for a tiny fraction of the cost.

If we shrink down the size of the active segment of the market, it becomes easier for that segment to earn its fees through the liquidity that it provides–which it has to do in order to collapse the arbitrage, particularly if its fees are going to remain high as a percentage of its assets. That is the path to an equilibrium in which active and passive generate the same return, net of fees, and in which there is no longer a reason to prefer one over the other.

Summary: Putting Everything Together

The points that I’ve tried to express in this piece are complex and difficult to clearly convey. So I’m going to summarize them in bullet points below:

The right size of the active segment of the market is the size that allows it to earn whatever fees it charges. If it cannot earn those fees, then there will always be an arbitrage opportunity putting pressure on its size. Investors will be able to get higher returns by going passive, and so that’s what they’ll do.

The only way the active segment, as a group, can earn its fees, is by providing liquidity to the market, specifically to the passive segment, and to corporations seeking new funding. All other profits for the segment will be zero-sum.

The question that determines the necessary amount of active management is this: how much natural passive flow is there in the system, i.e., non-speculative flow associated with people wanting to save excess income, or wanting to consume out of savings, or wanting to alter their risk allocations, given changes in their ages? Similarly, what is the natural corporate demand for funding? That flow, and that demand for funding, represents active management’s potential market for the provision of liquidity. Relative to the actual volume that takes place in the current market, it is minimal.

If the investing ethos evolves such that market participants become decreasingly inclined towards active behaviors–i.e., if they learn their lessons, and stop making trades for speculative reasons, and instead take the sage advice of a Bogle, or a Malkiel, or a Fama to limit their interventions to cases where they have legitimate non-speculative reasons for modifying their portfolios–then the active segment will have to shrink dramatically from its current size. Either that, or it will have to shrink its fees.

At some point in the above scenario–which, to be clear, is the Indexville scenario–the system will get to down to some bare-bones minimum level of active management, a level at which active managers, as a group, will be small enough to earn excess profits that are sufficient to cover the percentage-based fees they charge. Where is that minimum level? In my view, far away from the current level, at least at current fee rates. If I had to randomly guess, I would say somewhere in the range of 5% active, 95% passive. If we include private equity in the active universe, then maybe the number is higher–say, 10% active, 90% passive.

On the other hand, if we assume that the trend towards “passive investing” is simply about investors in the current bull market falling in love with $SPY or $VFIAX given the recent performance of U.S. equities, rather than about investors actually committing to the advice of a Bogle, or a Malkiel, or a Fama–then the future liquidity that those investors will consume when they change their minds will provide opportunities for what we’re calling the “active segment” to step in and earn its fees. But this point will be purely definitional, because the investors we are calling “passive”, though technically passive relative to the S&P 500, will not have been genuinely passive at all, in terms of the spirit of what that term means. They will have been active investors operating in guise, who just-so-happened to have been using index-based instruments in their efforts.

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The prior piece received a much stronger reaction than I expected. The topic is complicated, with ideas that are difficult to adequately convey in words, so I’m going to use this piece as a follow-up. I’m going to look at the specific example of the Tech Bubble, which is a clear case in which the broad adoption of a passive approach would have removed negative skill from the market and substantially increased market efficiency. I’m also going to offer some thoughts on the topics of differential liquidity, niche ETFs, and the drivers of inefficiencies in the area of asset allocation.

To begin, let me offer a brief comment on the topic of market efficiency. Recall the definition:

Efficiency: The extent to which all securities in a market are priced to offer the same expectedrisk-adjusted future returns.

In this definition, we have to emphasize the term “expected” because returns have a random component, and investors can only evaluate returns based on information that is available to them at the time. We also have to emphasize the term “risk-adjusted”, particularly when we try to talk about “efficiency” in terms of the relative pricing of securities that have different risk profiles–think: equities, bonds, cash. We don’t expect an efficient market to price these asset classes for the same return, but we do expect any differences in return to be justified by other differences in the securities: differences in liquidity, volatility, loss potential, and so on.

Sometimes, you will see the term “efficiency” defined in terms of the relationship between a security’s price and its future cash flows. For example:

Efficiency: The extent to which a security’s price matches the discounted sum of its future cash flows.

But this definition is not helpful, as the discount rate is not specified. Any cash-producing security can be described as “efficiently” priced if we get to “make up” our own discount rates from nothing. Now, to improve on the definition, we have the option of imposing the constraint that discount rates be applied consistently across different securities. But then the definition reduces to the original definition, because a “discount rate” is nothing more than a required rate of return for an investor. When we require that all cash flows in a space be discounted using the same rate, we are requiring that all securities offer the same rate of return, which is exactly where we started with the original definition.

The original definition of efficiency, which is the definition proposed by the person that invented the concept, is the best one for current purposes, because it directly connects “efficiency” with the concept of it being impossible to outperform in a space through active security selection. Pick whatever securities you want in a space. If the space is efficient, you will not be able to outperform, because every security you might pick will be offering the same return, adjusted for risk, as every other security.

Now, in the piece, I tried to make the following argument:

Passive investing increases the efficiency of the space in which it is being used.

I underline that last part because it’s crucial. Passive investing does not increase the efficiency of spaces in which it is not being used, nor should we expect it to. To use an example, investors might be bullish on U.S. equities relative to other asset classes. They might express that bullishness using $SPY. But the passivity of $SPY is incidental to what they’re doing. They are expressing an active preference–a preference to overweight large cap U.S. equities and underweight everything else–using a passive vehicle. The end result, a situation in which large cap U.S. equities are overvalued relative to everything else, would have been no different if they had expressed that same preference using an active vehicle–say, Fidelity Magellan fund. Nor would it have been any different if they had simply gone into the space of large cap U.S. equities and made the picks themselves, based on whatever they happened to like. The cause of the inefficiency has nothing to do with the passive or active nature of the vehicle used, and everything to do with the underlying bullish view that is driving its use–a view that is not passive, and that we are assuming is also not justified.

Now, the primary difference between using a passive vehicle and an active vehicle to express a view lies in the relative impact on the names inside the space that the vehicle is being used in. The passive vehicle will tend to have a minimal relative impact, because it is buying a small amount of everything in the space, in proportion to the amount in existence. The active vehicle will have a larger relative impact, because it is buying only what the manager–or the stock-picker–likes in the space.

To make the point maximally precise, suppose that the space in question is the space of [All U.S. Equities]. Note that when I put the term in brackets, I mean to refer to it as a space, a collection of securities:

We’re comparing two different ways of investing in [All U.S. Equities], active and passive. To invest actively in that space is to go in and buy whatever securities inside the space you happen to like, those that you think will perform the best. To invest passively in the space is to own a little bit of everything in the space, in proportion to its supply, i.e., the “amount” of it in the space, i.e., its”weighting.”

When an unskilled or negatively skilled participant chooses to invest actively in [All U.S. Equities], he reduces the efficiency of the space. He makes bad relative picks. In doing so, he creates opportunities for other participants, those that do have skill, to make good relative picks at his expense, as his counterparties.

To illustrate using the momentum factor, suppose that we have an unskilled or negatively skilled participant whose strategy is to buy those stocks that have gone down the most over the last year.

“When I invest, I keep it simple! I look for whatever is the most on sale! The biggest and best bargains!”

This participant has no understanding of the fundamentals of the companies he ends up buying, no understanding of the attractiveness or unattractiveness of their valuations as businesses, and no knowledge of the momentum patterns that markets have historically tended to exhibit on 1 year lookback periods. All he knows is the price–the more it has fallen, the more he wants to buy. Obviously, this participant is going to create opportunities for skilled participants–those that are familiar with the fundamentals and valuations of the companies being traded, and that are aware of the market’s historical momentum patterns–to outperform at his expense.

To be fair, maybe you don’t believe that there is such a thing as “skill” in a market. If that’s the case, then ignore what I’m saying. You will already be an advocate of passive investing–anything else will be a waste of time and money on your view. The argument, then, is not directed at you.

Now, suppose that Jack Bogle, and Burton Malkiel, and Eugene Fama, and the Behavioral Economists, and the robo-advisors, and so on, manage to convince this participant that he should not be investing in [All U.S. Equities] by making picks in the space himself–either of individual stocks or of expensive managers–but should instead be investing in the space passively–for example, by buying $VTI, the Vanguard Total U.S. Equity Market ETF. To the extent that he takes their advice and does that, he will no longer be introducing his flawed stock-picking strategy into the space, where other investors are going to exploit it at his expense. The efficiency of the space–i.e., the difficult of beating it through active security selection–will therefore increase.

Unfortunately, this is the place where things get muddled. If we’re talking about the space of [All U.S. Equities], then passive investing, to the extent that it is preferentially used by lower-skilled participants in that space, will increase the space’s efficiency. But, apart from that increase, it will not increase the efficiency of other spaces–for example, the broader space of [All U.S. Securities], where:

[All U.S. Securities] = [U.S. Equities, U.S. Bonds, U.S. Cash].

To illustrate, suppose that investors get wildly bullish on U.S. equities, and try to allocate their entire portfolios into the space, all at the same time. Suppose further that the lower-skilled participants of this lot, in making the move, choose to heed the advice of the experts. They shun the option of picking winners themselves, and instead buy into a broad equity index fund–again, $VTI. Their approach will be passive relative to the space of [All U.S. Equities], but it will not be passive relative to the space of [All U.S. Securities]. Relative to [All U.S. Securities], it will, in fact, be extremely active.

If lower-skilled participants express their demand for U.S. equities by buying $VTI rather than picking stocks in the space themselves, they will have eliminated the market inefficiencies that their picks inside that space would otherwise have introduced. Consequently, the efficiency of the space of [All U.S. Equities] will increase.

But, and this is the crucial point: beyond that increase, the space of [All U.S. Securities] will not become more efficient. That’s because the approach of putting an entire portfolio into $VTI is not a passive approach relative to [All U.S. Securities]. Relative to that space, the approach is just as active as the approach of putting an entire portfolio into Fidelity Magellan, or an entire portfolio into [$FB, $AMZN, $NFLX, $GOOG] “because I buy what I know.” U.S. Equities will still get expensive in comparison with other asset classes, because a preferential bid is still being placed on them. The fact that a passive vehicle, rather than an active one, is being used to place the bid is not going to change that result.

Now, a great example to use to concretely convey this point is the example of the market of the late 1990s. Hopefully, we can all agree that that the market of the late 1990s had two glaring inefficiencies:

Inefficiency #1: In the space of [All U.S. Equities], some stocks–for example, new-economy technology stocks–were wildly expensive, well beyond what a rational analysis could every hope to justify. Other stocks–for example, stocks with ties to the old-economy–were reasonably valued, especially in the small cap space. You could have outperformed the market by buying the former and shorting the latter, and you could have known that at the time, assuming you weren’t drinking the kool-aid. Therefore, the market was inefficient.

Inefficiency #2: In the space of [All U.S. Securities], which again consists of [All U.S. Equities, All U.S. Bonds, All U.S. Cash], the U.S. Equities component, as a group, was much more expensive than the other two asset classes, priced for much lower returns, especially after adjusting for the dramatically higher levels of risk. Again, you could have outperformed the market by holding cash and bonds, shunning equities, and you could have known that at the time, assuming you weren’t drinking the kool-aid. Therefore, the market was inefficient.

Recall that back then, passive investing wasn’t even close to being a “thing.” In fact, it was frowned upon:

“Vanguard? What? Why would you want to dilute your best holdings with companies that don’t have the potential to grow in the new economy? Doing that will significantly reduce your returns.”

“Yes, you need to diversify. But there’s a way to do it without sacrificing growth. What you need to do is this: mix your more established growth names–e.g., your Microsofts, your Intels, your Ciscos, your Yahoos, basically, the reliable blue chip stuff–with higher-risk bets–something like an Astroturf.com, or an Iomega, or a JDS Uniphase, that will offer high-powered upside if things work out for those companies. That will give your portfolio balance, without sacrificing growth. And if you need someone to help you set that up, we can certainly help you do that.”

Remember?

Since then, passive investing has become significantly more popular–so much so that a number of top investors have publicly described it as a “bubble” unto itself. And to be fair to those investors, the increased popularity does have certain bubble-like characteristics. Gurus on TV advocating it? Check. New companies springing up to exploit it? Check. Rapid increase in AUM? Check.

Now, suppose that passive investing had been as popular in 1999 as it is today. Instead of expressing their cyclical equity bullishness by utilizing their own stock-picking expertise–or their expertise in picking stock-pickers, which was just as flawed, evidenced by the fact that everyone was piling into the same unskilled Technology managers–suppose that investors had simply used a broad market index fund: say, $VTI. What would the impact have been?

With respect to inefficiency #2–i.e., the inefficiency that saw the U.S. equity market wildly overvalued relative to other asset classes–that inefficiency might not have been ameliorated. Bullishness for an asset class tends to lead to overvaluation, regardless of the vehicles used to express it, whether passive ($VTI) or active (Fidelity’s top performing fund, you going into your E-Trade account and buying into a stock that your friend at work just made a bunch of money on).

But inefficiency #1–the inefficiency that saw certain parts of the U.S. equity market trade at obnoxious prices, while other parts traded quite reasonably–would definitely have been less severe. It would have been less severe because the segment of the market that was doing the most to feed it–the lower-skilled retail segment that, in fairness, didn’t know any better–wouldn’t have been playing that game, or feeding that game by picking unskilled managers who were playing it.

This example, in my view, is a perfect example of how the widespread adoption of a passive approach can make a market more efficient. Granted, it can only do that in the specific space in which it is being used. Right now, it’s not being appreciably used in the broad space of [All U.S. Securities] or [All Global Securities]. But it is being used in the space of [All U.S. Equities]. We can debate the degree–and I acknowledge that the effect may be small–but I would argue to you that the use has made the space more efficient, even as we speak.

If you disagree, then do this. Go find your favorite value investor, and ask him what his biggest gripe right now is. This is what he will tell you:

“The problem with this market is that everything is overvalued. Everything! In 1999, I was able to hide out in certain places. I was able to find bargains, especially on a relative basis. Right now, I can’t find anything. The closest thing to an opportunity would be the energy sector, but that sector is only cheap on the assumption of a rebound in energy prices. If we assume that prices are not going to rebound, and are going to stay where they are for the long-term, then the typical energy name is just as expensive as everything else in the market. Yuck!”

Here’s a question: what if that the widespread embrace of a passive approach with respect to U.S. equities in the current cycle is part of the reason for the broadness of the market’s expensiveness? Personally, I don’t know if that’s part of the reason. But it certainly could be.

Now, before you point to that possibility as evidence of the harm of passive investing, remember the definition of efficiency:

Efficiency: The extent to which all securities in a market are priced to offer the same expectedrisk-adjusted future returns.

On the above definition of “efficiency”, an expensive market that gives investor no way to escape the expensiveness–e.g., the 2013-2016 market–is actually more efficient than an expensive market with large pockets of untouched value–e.g., the 1999 market. If the increased popularity of passive investing has, in fact, reduced the dispersion of valuation across the U.S. equity space–the type of dispersion that lower-skilled participants would be more inclined to give support to–then the outcome is consistent with the expectation. Passive investing has caused the U.S. equity market to become more efficient, harder to beat through active security selection. The suckers have increasingly taken themselves out of the game, or have been increasingly forced out of the game, leaving the experts to fight among themselves.

A number of investors seem to want to blame passive investing for the fact that U.S. equities are currently expensive. Doing that, in my view, is a mistake. The expensiveness of U.S. equities as an asset class is not a new condition. It’s a condition that’s been in place for more than two decades–long before passive investing became a “thing.” If you want to blame it on something, blame it on Fed policy. Or better yet, blame it on the causes of the low-inflation, low-growth economic condition that has forced the Fed to be accomodative, whatever you believe those causes to be. The Fed has responded entirely appropriately to them.

It’s hard to blame the current market’s expensiveness entirely on the Fed, because there was a long period in U.S. history when the Fed was just as easy as it is today–specifically, the period from the early 1930s through the early 1950s. In that period, equities did not become expensive–in fact, for the majority of the period, they were quite cheap. Of course, that period had an ugly crash that damaged the investor psyche, at least in the earlier years. But the same is true of the current period. It has had two crashes, one with a full-blown crisis. Yet our market hasn’t had any problem sustaining its expensiveness.

If we had to identify an additional factor behind the market’s current expensiveness, one factor worth looking at would be the democratization of investing. Over the last several decades, investing in the market has become much cheaper in terms of the transaction costs, and also much easier in terms of the hoops that the average person has to jump through in order to do it. It makes sense that this development would increase participation in the equity markets, and therefore increase prices.

Does it make sense to hold cash at an expected future real rate of, say 0%, when you can invest in equities and earn the historical real rate of 6%? Clearly not. In a period such as the late 1940s, the barriers to having a broad section of the population try to arbitrage away that differential may have been large enough to keep the differential in place. But today, with all of the technological innovation that has since occurred, the barriers may no longer be adequate. A 6% equity risk premium may simply be too high, which would explain why it has come down and stayed down. To be honest, I’m not fully convinced of this line of reasoning, but it’s worth considering.

Returning to the current discussion, it’s important not to confuse the democratization of investing–the development of broad online access to investment options at negligible transaction costs–with the increased popularity of passive approaches. These are fundamentally different phenomena.

It may be the case that in the current cycle, investors are using the familiar passive vehicles–$SPY and $VFIAX–to drive up the market. But so what? The passivity of the vehicles is not what is fueling the move. What’s fueling the move is the bullish investor sentiment. If, instead of being sold on the wisdom of a passive approach, investors were skeptical of it, then they would simply express their bullishness actively, piling into popular active mutual funds, or picking stock themselves–which is exactly what they did in 1999, long before the average investor even knew what $SPY was.

Before concluding, let me briefly address a few caveats:

First, liquidity. Passive vehicles are not sensitive to differentials in liquidity. So, to the extent that those differentials exist across a space, widespread use of passive vehicles in a space can create exploitable distortions.

To give an example, if a micro-cap ETF sees net inflows, it’s going to use those net inflows to make purchases in the space. Given its passive approach, the specific purchases will be spread across the space, regardless of the liquidity differences in the individual names. So, if there is a part of the space that is highly illiquid, prices in that part will get pushed up more than in other parts, creating a potential inefficiency.

If net flows go back and forth into the micro-cap ETF, it will engage in costly round-trips in the illiquid security, thereby losing money to active participants in the market–specifically, those that are making a market in the illiquid security. In contrast with a passive ETF, an active ETF or mutual fund can avoid this outcome because it is able to direct its purchases towards liquid areas of a market, or at least factor the cost of illiquidity into its evaluations of potential opportunities.

As a rule, passive vehicles tend to generally be less “disruptive” in their purchases than active vehicles because they buy securities in proportion to the supply of shares outstanding. In a sense, the demand they inject is intrinsically tethered to the available supply. One caveat noted by @SmallCapLS, however, is that the actual supply that matters, the floated supply in the market, may be different from the total shares outstanding, which is what determines the weighting. In situations where the float is tiny, and the outstanding share count very large, passive vehicles have the potential to be more disruptive.

The market impacts of these potential liquidity-related inefficiencies are minimal. Not worth worrying about, especially for those investors that are not involved in illiquid spaces.

Second, niche ETFs. No one has raised this specific objection, but after thinking the issue through, it would be hard to deny that certain highly niche ETFs–for example, the proposed 3-D printing ETF $PRNT–have the potential to create distortions, if not simply by giving inexperienced investors bad ideas, i.e., suckering them into making bets on spaces that they should not be making bets on. But again, we shouldn’t pin the distortions onto the passivity of the funds. With repect to 3D printing, for example, there’s an active mutual fund that offers (or offered) the exact same exposure: $TDPNX, the 3D Printing, Robotics, and Tech Investment fund. If you look at the active mutual fund graveyard of the last 20 years, you will find plenty of the same types of funds, each of which managed to pull investors into a fad at exactly the wrong time. It’s not a passive vs. active thing, but a feature of the business–gather assets, in whatever way works.

Third, when I said that nobody is using a passive approach relative to the broader space of global securities–i.e., all foreign and domestic equities, all foreign and domestic bonds, all foreign and domestic cash, owning each passively, in proportion to its outstanding supply–I did not mean to say that this could never be done. It can definitely be done–there just isn’t a demand to do it.

Consider a hypothetical ETF–we’ll call it $GLOBE. $GLOBE holds every liquid financial asset in existence, including currencies, in relative proportion to the supply in existence. Right now, investors don’t have an easy $GLOBE option–the closest option would be a robo-advisor. The difference between $GLOBE and a robo-advisor, however, is that the robo-advisor uses a predefined allocation–e.g., 60% stocks, 40% bonds/cash–as opposed to a “market” allocation that is based on the outstanding supplies of the different asset classes.

Using a pre-defined allocation can create inefficiencies in cases where the supply of one of the asset classes is naturally tighter than the other. When everyone tries to allocate in such a configuration, the tighter asset class gets pushed up in relative price and valuation, resulting in a potential inefficiency. The dynamics of this process were discussed in more detail in a prior piece.

Returning to $GLOBE, in my view, a liquid fund in the mold of $GLOBE, if it caught on with the lower-skilled segment of the market, would make the market more efficient, not less. Unskilled investors would be able to use the vehicle to remove their unskilled timing and rotation decisions from the market fray, reducing the opportunities of skilled investors to outperform at their expense. In truth, the effect on broad market efficiency would probably be very small, if perceptible at all. Regardless, markets would not be made any less efficient by it, as opponents of passive approaches want to suggest.

As markets continue to develop and adapt going forward, the investment area that I suspect will be the most likely to continue to present inefficiencies is the area of asset allocation. Asset allocation is an area where a passive stance is the most difficult to fully embrace. The temptation to try to “time” asset classes and “rotate” through them in profitable ways can be quite difficult to resist, particularly when conditions turn south. Unlike the game of individual stock-picking, lower-skilled investors are not likely to want to voluntarily take themselves out of that broader game–in fact, of all market participants, they may be the least inclined to want to do so.

Decisions on how to allocate among broad asset classes–equities, fixed income, and especially cash–are among the least professionally-mediated investment decisions that investors make. If you want to invest in U.S. equities, there are tons of products available to help you. These products eliminate the need for uninformed participants to make relative bets inside that space.

But the decision of what asset classes to invest in more broadly, or whether and when to invest at all–whether to just keep the money in the bank, and for how long–is a decision that is much more difficult to offload onto someone else, or onto a systematic process. Even if an advisor is used, the client still has to make the decision to get started, and then the decision to stick with the plan. “The stock market is doing really well, at all time highs. But I’m not invested. Should I be?” “This isn’t working. Our stuff is really down a lot. Are we in the right setup here?” Naturally, we should expect a space in which unskilled investors are forced to make these decisions for themselves–without experts or indices to rely on–to exhibit greater inefficiency, and greater opportunity.

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U.S. equity index funds have grown dramatically in recent decades, from a negligible $500MM in assets in the early 1980s to a staggering $4Ttoday. The consensus view in the investment community is that this growth is unsustainable. Indexing, after all, is a form of free-riding, and a market can only support so many free-riders. Someone has to do the fundamental work of studying securities in order to buy and sell them based on what they’re worth, otherwise prices won’t stay at correct levels. If too many investors opt out of that work, because they’ve discovered the apparent “free lunch” of a passive approach, active managers will find themselves in an increasingly mispriced market, with greater opportunities to outperform. These opportunities will attract funds back into the actively-managed space, reversing the trend. Or so the argument goes.

In this piece, I’m going to challenge the consensus view. I’m going to argue that the trend towards passive management is not only sustainable, but that it actually increases the accuracy of market prices. It does so by preferentially removing lower-skilled investors from the market fray, thus increasing the average skill level of those investors that remain. It also makes economies more efficient, because it reduces the labor and capital input used in the process of price discovery, without appreciably impairing the price signal.

The Irrelevance of Passive Share: A Concrete Example

There’s an important logical rule that often gets missed, or at least misunderstood, in discussions on the merits of active and passive management. The best way to illustrate that rule is with a concrete example. Consider a hypothetical market consisting of 100 different individual participants. Each participant begins the scenario with an initial portfolio consisting of the following 5 positions:

100 shares of Facebook ($FB)

100 shares of Amazon ($AMZN)

100 shares of Netflix ($NFLX)

100 shares of Google ($GOOG)

$100,000 in cash.

We assume that these financial assets represent all financial assets in existence, and that the market is closed, meaning that new financial assets cannot enter or be created, and that existing financial assets cannot leave or be destroyed. With each participant in possession of her initial portfolio, we open the market and allow trading to take place.

Now, in the first scenario, we assume that 10 out of the 100 participants choose to take a passive approach. These participants recognize that they lack the skill necessary to add value through trading, so they opt to simply hold their initial portfolios as received. The other 90 participants choose to take an active approach. They conduct extensive fundamental research on the four underlying companies, and attempt to buy and sell shares based on their assessments of value. Naturally, their assessments change as new information is received, and so the prices change.

Suppose that we mark the price of each security to market on December 31, 2016 and then again on December 31, 2017.

(Note: these prices do not represent predictions or investment advice)

We use the prices to determine the aggregate and average returns of the passive and active segments of the market. The result:

As the table shows, the returns of the active and passive segments of the market end up being identical, equal to 7.7%. The reason the returns end up being identical is that the two segments are holding identical portfolios, i.e., portfolios with the same percentage allocations to each security. The allocations were set up to be the same at the outset of the scenario, and remain identical throughout the period because the two segments do not trade with each other. Indeed, the two segments cannot trade with each other, because the passive segment has decided to stay passive, i.e., to not trade.

To be clear, the individual members of the active segment do trade with each other. But their trades are zero-sum–for every share that an active investor buys, some other active investor is selling those exact same shares, and vice-versa. Consequently, the aggregate “position” of the active segment stays constant at all times. Because that position was initially set to be equal to the aggregate position of the passive segment, it stays equal for the entire period, ensuring that the aggregate returns will be equal as well.

Now, the consensus view is that if too many investors try to free-ride on a passive strategy, that the securities will become mispriced, creating opportunities for active investors to outperform. To test this view, let’s push the scenario to an extreme. Let’s assume that in the second scenario 98 of the investors initially opt to remain passive, with only two opting to trade actively.

Will the decrease in the number of active investors–from 90 in the first scenario down to 2 in the second–make it any easier for those investors to outperform as a group? Not at all. The two investors that make up the active segment are going to have trade with each other–they won’t have anyone else to trade with. Regardless of how they trade, their combined portfolios will remain identical in allocation to the combined portfolios of the 98 investors that are passively doing nothing. The performances of the two segments will therefore remain the same, just as before. This fact is confirmed in the table below, which shows both segments again earning 7.7%:

The Law of Conservation of Alpha

The prior example illustrates a basic logical rule that governs the relationship between the aggregate performances of the active and passive segments of any market. I’m going to call that rule “The Law of Conservation of Alpha.” It’s attributable to Eugene Fama and William Sharpe, and can be formally stated as follows:

The Law of Conservation of Alpha (Aggregate): The aggregate performance of the active segment of a market will always equal the aggregate performance of the passive segment.

Importantly, this rule applies before frictions are taken out–management fees, transaction costs, bid-ask spread losses, taxes, and so on. Because the passive segment of a market tends to experience less friction than the active segment, the passive segment will typically outperform the active segment.

Now, the aggregate return of a group and the (asset-weighted) average return of each member of that group are essentially the same number. We can therefore reframe the rule in terms of averages:

The Law of Conservation of Alpha (Average): Before fees, the average performance of the investors that make up the active segment of a market will always equal the average performance of the investors that make up of the passive segment.

The terms “active” and “passive” need to be defined. An “active” allocation is defined as any allocation that is not passive. A “passive” allocation is defined as follows:

Passive Allocation: An allocation that holds securities in relative proportion to the total number of units of those securities in existence.

Crucially, the term “passive” only has meaning relative to a specific universe of securities. The person using the term has to specify the securities that are included in that universe. In our earlier example, the universe was defined to include all securities in existence, which we hypothetically assumed to be $10MM U.S. dollars and 10,000 shares each of four U.S. companies–Facebook, Amazon, Netflix and Google. In the real world, many more securities will exist than just these. If we were to define the term “passive” to include all of them, then a “passive” portfolio would have to include all equity shares, all fixed income issues, all money in all currencies, all options, all warrants, all futures contracts, and so on–each in proportion to the total number of units outstanding. And if we were to include non-financial assets in the definition, a “passive” portfolio would have to include all real estate, all precious metals, all art work, and so on–anything that has monetary value unrelated to present consumption. The problem of determining the true composition of the “passive” segment of the market would become intractable, which is why we have to set limits on the universe of securities that we’re referring to when we speak of a “passive” approach.

To illustrate how we would build a passive portfolio, let’s focus on the universe of the 30 companies that make up the Dow Jones Industrial Average (“The Dow”). To establish a passive allocation relative to that universe, we begin by quantifying the total number of existing shares of each company. We then arbitrarily pick a reference company–in this case, 3M ($MMM)–and calculate the respective ratios between the number of shares outstanding of each company and that company, $MMM. The ratios will determine the relative number of shares of each company that we will hold (see the right column below):

You can see in the chart that Home Depot ($HD) has 2.07 times as many shares outstanding as $MMM. So, in our passive portfolio, we hold 2.07 times as many shares of $HD as $MMM. And 6.79 times as many shares of Exxon-Mobil ($XOM). And 13.07 times as many shares of Microsoft ($MSFT). And so on.

Note that this formula doesn’t specify the absolute number of shares of each company that we would need to hold in order for our portfolio to be “passive.” Rather, it specifies the relative ratio of number of shares of each company that we would need to hold. In practice, we will choose the absolute number of shares that we hold based on the amount of wealth that we’re trying to invest in the passive strategy.

Now, mathematically, if we hold a share count of each security that is proportionate to the total number of shares in existence, we will also end up holding a market capitalization of each security–share count timesprice–that is proportionate to the total amount of market capitalization in existence. This will be true regardless of price, as illustrated in the table below:

The table assumes you hold 1 share of $MMM, and therefore, by extension, 1.57 shares of American Express ($AXP), 8.93 shares of Apple ($AAPL), 1.07 shares of Boeing ($BA), and so on. The prices of these securities determine both your allocation to them, and the aggregate market’s allocation to them, where “allocation” is understand in terms of market capitalization. In the table above, the allocations–for both you and the market–end up being 1.89% to $MMM, 11.01% to $AAPL, 1.58% to $BA, and so on.

Obviously, prices will change over time. The changes will cause changes in the aggregate market’s percentage allocation to each security. But you won’t need to worry about those changes, because they will pass through to your allocation as well. The price changes will affect your allocation in the exact same way that they affect the aggregate market’s allocation, ensuring that the two allocations remain identical in market capitalization terms–provided, of course, that you remain passive and refrain from trading.

A passive strategy is special because it is the only type of strategy that can remain in place in the presence of price changes without requiring investor action. No other investment strategy is like that–value, momentum, pre-defined allocation, etc.–these strategies all require periodic “rebalancing” in order to preserve their defining characteristics. A value portfolio, for example, has to sell cheap stocks that become expensive, and buy expensive stocks that become cheap, otherwise it will cease to meet the definition of “value.” A momentum portfolio has to sell high-momentum stocks that lose momentum, and buy low-momentum stocks that gain momentum, otherwise it will cease to meet the definition of “momentum.” A 60/40 stock/bond portfolio has to sell the asset class that appreciates the most, and buy the asset class that appreciates the least, otherwise it will cease to be a 60/40 portfolio, and will instead become a 63/37 portfolio, or a 57/43 portfolio, and so on. A passive portfolio, in contrast, can completely ignore any and all price changes that occur–it will remain “passively” allocated, i.e., allocated in proportion to the overall market supply, no matter what those changes happen to be.

Accounting Complications: A Solution

When we try to apply The Law of Conservation of Alpha to actual market conditions, we run into accounting complications. For an illustration, consider the following sample of portfolios in the market:

How exactly would one go about applying the Law of Conservation of Alpha to these portfolios? Recall the law itself:

The Law of Conservation of Alpha (Average): Before fees, the average performance of the investors that make up the active segment of a market will always equal the average performance of the investors that make up of the passive segment.

Look closely at the U.S. Equity Indexer’s portfolio. The single position is expressed passively through an S&P 500 mutual fund, $VFIAX. We might therefore call it “passive.” But it clearly isn’t “passive” with respect to the overall universe of existing securities, as there are many more securities in the world than just the equities contained in the S&P 500.

Of course, if we limit our universe to S&P 500 equities, then the U.S. Equity Indexer’s portfolio is passive (relative to that universe). According to the Law of Conservation of Alpha, the portfolio’s performance will match the average performance of active managers that play in that same universe, i.e., active managers that own stocks in the S&P 500. The problem, of course, is that the investment community cannot be cleanly separated out into “active managers that own stocks in the S&P 500.” Many of the managers that own stocks in the S&P 500 universe, such as the Value Investor shown above, also own securities that do not fall into that universe. In aggregate, their portfolios will not be identical to the S&P 500 in terms of allocation, and therefore the performances will not match.

Fortunately, there’s a way around this problem. If our universe of concern is the S&P 500, then, to apply The Law of Conservation of Alpha to that universe, we identify all portfolios in the market that hold positions in S&P 500 constituents, long or short. Inside each of those portfolios, we group the positions together, bracketing them out as separate entities with their own separate performances–“S&P 500 component funds” whose returns can be evaluated independently. To illustrate, the S&P 500 component funds for the above portfolios are boxed in the image below:

To be clear, what we’re doing here is taking the securities in each portfolio that fall inside the S&P 500, and conceptually bracketing them out as separate vehicles to be analyzed–separate S&P 500 component funds to be tracked. Some of the S&P 500 component funds in the group–for example, that of the U.S. Equity Investor who holds $VFAIX, and that of the Robo-Advisor who holds $SPY–are passively allocated relative to the S&P 500. The allocations of those funds are identical to the allocation of the S&P 500, which is why we’ve boxed them in green. Similarly, other S&P 500 component funds–for example, that of the Day Trader whose only S&P 500 holdings consist of Facebook, Amazon, Netflix, and Google, in equal market cap proportion–are actively allocated relative to the S&P 500. The allocations of those funds actively deviate from the allocation of the S&P 500, which is why we’ve boxed them in red.

We can reframe the Law of Conservation of Alpha in terms of component funds as follows:

The Law of Conservation of Alpha (Average, Component-Basis): For a given universe of securities, the average performance, before fees, of all active component funds associated with that universe will always equal the average performance, before fees, of all passive component funds associated with that universe.

Put simply, what the law is saying is that if we properly identify and delineate the active and passive component funds of a given universe in every portfolio, summing the active together and the passive together, the respective allocations to each security of the active and passive sums will be equal at all times. It follows that the aggregate returns of the active and passive sums will be equal, before fees.

The Impact of Net Fund Flows

Consider the Vanguard S&P 500 index fund, $VFIAX. What happens when it receives a net cash inflow? The answer: it ceases to be allocated passively relative to the S&P 500. It ends up owning cash, a security not contained in the S&P 500. To become passive again, it has to go into the market and trade that cash for S&P 500 shares, in exact proportion to the amount in existence. Until it does that, it will technically be in an active stance.

By coincidence, when it goes into the market, it may end up making the purchases from other S&P 500 index funds that are experiencing equivalent net cash outflows. If that happens, then the transactions will be a wash for the passive segment of the market, and can be ignored.

If, however, there aren’t matching S&P 500 index fund outflows for it to pair up with and offset, then it will have to transact with the active segment of the market. It will have to go into the market and buy shares from the active segment, becoming the active segment’s counterparty. Whenever the two segments of the market–active and passive–become counterparties to each other, the previous logic ceases to apply. It becomes possible for the active segment of the market to outperform the passive segment, in what might seem like a contradiction of The Law of Conservation of Alpha.

Importantly, The Law of Conservation of Alpha is only meant to apply once a passive portfolio has already been established. If a passive portfolio is in place, and stays in place continuously for a period (because the passive investor refrains from trading), then the performance of the passive portfolio during that period will match the aggregate performance of the market’s active segment during that period. The performances need not match in periods before the passive portfolio is established, or in periods after the passive portfolio has been lost through cash inflows and outflows.

So there you have the exception to the rule. The performances of the active and passive segments of the market can deviate during those periods in which the passive segment is not truly passive. In practice, however, such deviations will be small, because index funds act reasonably quickly to preserve their passive stance in response to net inflows and outflows–too quickly for the index to move away from them in either direction. What they primarily lose to the active segment is the bid-ask spread. Each time they buy at the ask, and sell at the bid, they give half of the associated spread to the active segment of the market, which includes the market makers that are taking the other sides of their orders. The loss, however, tends to be miniscule, or at least easily offset by the other profit-generating activities that they engage in (e.g., securities lending), evidenced by the fact that despite having to deal with large flows, index funds have done a fantastic job of tracking their “pure” indexes. To offer an example, $VFIAX, the world’s largest passive S&P 500 index mutual fund, has tracked the S&P 500 almost perfectly over the years, which is why you only see one line in the chart below, when in fact there are two.

Now, to be clear, large net inflows and outflows into index funds can certainly perturb the prices of the securities held in those funds. And so if, tomorrow, everyone decided to buy $VFIAX, the prices of S&P 500 companies would surely get bid up by the move. But the situation would be no different if investors decided to make the same purchase actively, buying actively-managed large cap U.S. equity funds instead of $VFIAX. The perturbation itself would have nothing to do with the passive structure of $VFIAX, and everything to do with the fact that people are attempting to move funds en masse into a single asset class, U.S. equities. Relative to the universe of all securities, that’s a decidedly “not passive” thing to do.

The key difference between using $VFIAX to buy large cap U.S. equities, and using actively managed funds for the same purpose, lies in the effect on the relative pricing of S&P 500 companies. The use of $VFIAX does not appreciably affect that pricing, because an equal relative bid is placed on everything in that index. The use of actively managed funds, in contrast, does affect the relative pricing, because the relative bid on each company in the index will be determined by which names in the index the active managers who receive the money happen to prefer.

Intuitively, people tend to get hung up on the idea that index funds could somehow be counterparties to active managers, and yet continue to track the aggregate performances (before fees) of those same active managers. The hangup is best illustrated with an example. Suppose that I have perfect market clairvoyance, and know, with certainty, that $FB is going to double over the next year. Obviously, I’m going to go into the market and buy as much $FB as I can. Suppose that in the actual transaction that ensues, I end up buying $FB from an S&P 500 index fund–say, $VFIAX–that happens to be experiencing a redemption request, i.e., a cash outflow.

When I buy $FB from $VFIAX, and $FB goes on to double, I’m obviously going to end up outperforming the S&P 500. Who, then, is going to underperform the S&P 500? Secondary market transactions are zero-sum games for the participants, so if I’m going to outperform, someone will have to underperform. The temptation is to say that $VFIAX is going to underperform, since it’s the one that’s foolishly selling the undervalued $FB shares to me. But, to the extent that $VFIAX is maintaining a passive stance, it’s going to handle the cash outflow by also selling all other stocks in the S&P 500, in exact relative proportion to the number of shares that exist. For every 1 share of $FB that it sells to meet the redemption, it’s also going to sell 2.36 shares of $AAPL, 0.414 shares of $AXP, 0.264 shares of $MMM, and and so on, all in order to preserve its passive allocation relative to the S&P 500. To the extent that it successfully preserves that allocation, its performance will continue to track the S&P 500’s performance.

Who, then, will underperform the S&P 500, to offset my outperformance? The answer: the rest of the active market. When $VFIAX sells the 500 stocks in the S&P 500, and I preferentially buy all the $FB shares that it’s selling, the rest of the active market will end up not buying those shares. It will be forced to buy all of the other names in the S&P 500 that $VFIAX is selling, with $FB left out. The rest of the market will therefore end up underweighting $FB relative to the S&P 500, offsetting my overweight. When $FB goes on to double, the rest of the market will therefore underperform relative to the S&P 500, offsetting my outperformance.

The example demonstrates that in a liquid market, passive index funds can easily do what they need to do, making the transactions that they need to make in order to maintain their passivity, without perturbing relative prices. If I try to overweight $FB and underweight everything else, then, in a normal market environment, the price of $FB should get bid up relative to everything else. That’s exactly what’s going to happen in the above example, because I will be removing the selling pressure that the $VFIAX outflow is putting on $FB, without removing the selling pressure that the $VFIAX outflow is putting on everything else. The $VFIAX outflow is entirely transparent to the market’s relative pricing mechanism, leaving prices just as they would have been in its absence.

Now, to be clear, in an illiquid market, with large bid-ask spreads, all bets are off. As we noted earlier, when a passive index fund receives inflows and outflows, and has to transact with the active segment to maintain its passive stance, it loses the bid-ask spread. If that spread is large, then there’s a viable pathway for active managers–specifically market-makers–to outperform at the passive fund’s expense.

The Impact of New Share Issuance and Share Destruction through Buybacks

A separate source of performance divergence emerges in the context of new share issuance. Suppose that a fund is employing a passive index strategy relative to the total universe of publicly traded U.S. equities–all sizes: large, medium, small, and micro. A new company then conducts an initial public offering (IPO). That company will immediately be part of the universe of publicly-traded equities. To maintain its passive allocation relative to that universe, the index fund in question will need to obtain a proportionate number of shares of the company. There may be a delay–potentially a significant one–between the time that the IPO occurs and the time that the fund actually obtains the shares. That delay will create a window for the fund’s performance to deviate from the performance of the market’s active segment.

Whether this type of divergence will result in outperformance or underperformance for index funds will depend on how newly issued securities tend to perform during the periods between their issuances and their entries into the index funds. If, as a group, newly issued securities tend to perform better than the rest of the market during those periods, then index funds will underperform the market accordingly. If, as a group, they tend to perform worse than the rest of the market during those periods, then passive funds will outperform the market accordingly.

Most passive funds have lower-limits on the market capitalizations of securities they hold–they only take in new companies when those companies reach certain sizes and levels of liquidity. The temptation is to therefore conclude that such funds will tend to underperform the active segment of the market, given that they are only buying newly issued securities after those securities have appreciated substantially in price, with the appreciation having accrued entirely to the gain of the active segment of the market that holds them in their infancy. This conclusion, however, ignores all of the newly issued securities that perform poorly after issuance. Passive funds are able to avoid the losses that those securities would otherwise inflict.

In terms of the impact on index performance relative to the market, what matters is not how newly issued securities that successfully make it into indices perform relative to the market, but how all newly issued securities perform relative to the market, including those that never make it into indices. In theory, we should expect newly issued securities to be priced so that their average performances end up roughly matching the average performance of the rest of the market, otherwise capitalist arbitrage would drive the market to issue a greater or lesser number of those securities, forcing a price adjustment.

Now, share buybacks create a similar challenge, but in reverse. If a company buys back its shares and retires them, then, to stay passively-allocated, an index fund that holds the shares is going to have to adjust its allocation accordingly–it’s going to have to sell down the position, and proportionately reallocate the proceeds into the rest of the index. The period prior to that adjustment will represent a window in which the fund is officially no longer passively-allocated, and in which its performance will have the potential to diverge from the performance of the market’s active segment. Whether the divergence will amount to outperformance or underperformance will depend on how companies perform relative to the rest of the market shortly after share buybacks occur.

To summarize, net flows, new share issuance and share destruction through buybacks can, in theory, create divergences between the performances of the passive and active segments of the market. But there’s little reason to expect the divergences to have a sizeable impact, whether favorable or unfavorable. In terms of a concrete application of the Law of Conservation of Alpha, they can typically be ignored.

Flawed Comparisons: Apples to Apples, Oranges, and Grapes

The theory here is well-understood, but when we compare the average performance of active funds over the last 10 years to the average performance of index funds over the same period, we find that active funds have somehow managed to underperform their passive counterparts by more than their cost differentials. Given the Law of Conservation of Alpha, how is that possible?

The answer, again, relates to inconsistencies in how asset universes get defined in common parlance, particularly among U.S. investors. When investors in the United States talk about the stock market, they almost always mean the S&P 500. But active equity funds routinely hold securities that are not in that index–small-caps, foreign companies, and most importantly, cash to meet redemptions. In an environment such as the current one, where the S&P 500 has dramatically outperformed these other asset classes, it goes without saying that active funds, which have exposure to the asset classes, are going to underperform in comparison. But this result says nothing about active vs. passive, as the comparison itself is invalid.

In a brilliant essay from last year, Neil Constable and Matt Kadnar of GMO proved the point empirically. They showed that the percentage of active large cap managers who outperform the S&P 500 is almost perfectly correlated with the relative outperformance of foreign equities, small-caps, and cash–the three main ex-S&P 500 asset classes that active large cap managers tend to own. The following chart, borrowed from their essay, illustrates:

If we clean up the discussion, and examine exposures on a component basis, we will find that the average active S&P 500 component fund in a portfolio–i.e., the average grouping of strictly S&P 500 companies inside a portfolio–performs the same, before fees, as the average passive S&P 500 index fund. This is always be true, no matter what the S&P 500 index or any other index happens to be doing.

But Who Will Set Prices?

Active investors set prices in a market. Passive investors can’t set prices, because they don’t trade securities on a relative basis. They hold all securities equally, in relative proportion to the total quantity in existence. They only make relative trades in those rare instances in which market activity forces them to–e.g., in response to new share issuance or share destruction through buybacks.

An efficient market needs active investors to be the ones setting prices, because active investors are the ones doing the fundamental work necessary to know what the securities themselves are actually worth. For this reason, we tend to be uncomfortable with the idea that a market could function properly if the majority of its investors decided to go passive. We worry that the active investors in such a market wouldn’t be able to control enough money and flow to effectively do their jobs.

Setting price in a market, however, isn’t about controlling a certain amount of money or flow. It’s simply about placing an order. If all other players in a market have opted to be passive and not place orders, then “price” for the entire market can effectively be set by the single individual investor who does place an order, no matter how small she may be in size.

Why Passive Investing Increases the Market’s Efficiency

The view that passive investing undermines market efficiency is intuitively appealing and therefore widespread. To quickly see the wrongness in the view, we need only ask ourselves the following question: is it any easier for a well-trained active stock-picker to beat the market today than it was in the early 1980s? By “well-trained”, I mean “well-trained” relative to the state of industry knowledge at the time. The answer, obviously, is no. It’s just as hard to beat the market today as it was back then–in fact, by the results alone, we might think that it’s actually harder. Yet the share of the market that is allocated passively has increased dramatically in the intervening period, a fact that is entirely inconsistent with the claim that passive indexing undermines market efficiency.

As it turns out, a much stronger argument can be made in favor of the view that passive investing increases market efficiency. Before I present the argument, let me first say a few things about the concept of “market efficiency.”

We define an efficient market as follows:

Efficient Market: For a given group of securities, a market is efficient with respect to that group if all securities in the group are priced to offer the same expected risk-adjusted future returns. In a broader sense, a market is unqualifiedly efficient if all of the securities traded within it are priced to offer the same expected risk-adjusted future returns.

To use an example, the group of 500 securities that comprise the S&P 500 represent an “efficient market” to the extent that every security in that group–$AAPL, $FB, $MMM, $XOM, and so on–is priced to offer the same expected risk-adjusted future return as every other security in the group. More broadly, the collection of assets that comprise the overall asset universe–all stocks, bonds, all cash, all real-estate, everywhere–represent an “efficient market” to the extent that every asset in existence is priced to offer the same expected risk-adjusted future return as every other asset in existence–admittedly, a very high hurdle.

Empirically, the test for an efficient market is straightforward: can an investor consistently outperform the average of a market by selectively picking individual securities in the market to preferentially own? If the answer is yes, then, necessarily, the individual securities in the market are not priced to offer the same expected risk-adjusted future returns, and therefore the market is not efficient. It’s important to emphasize the word “consistent” here, as returns have a random component. An investor in an efficient market can always make a lucky pick. What an investor in an efficient market cannot do is reliably make such a pick over and over again.

The way that a market becomes efficient is through arbitrage. If, for example, a given individual security in a market is offering a more attractive risk-adjusted future return than all of the other securities, and if investors know this, then they will try to buy that security, selling the others as necessary to raise funds. But not everyone can own the security in question, and therefore its price in the market will rise. As its price rises, its expected risk-adjusted future return will fall, bringing that return into congruence with the rest of the market.

We can think of this process as happening in two specific stages: source mistake and corrective arbitrage.

Source Mistake: The source mistake stage occurs when investors make trades that are fundamentally incorrect, e.g., when investors willingly buy securities at prices substantially above reasonable fair value, or willingly sell securities at prices substantially below reasonable fair value. An example: investors might grow psychologically anchored to the historical price level of a given stock, rigidly assessing the attractiveness of the stock’s current price relative to that level, without considering fundamental changes that might have recently taken place, such as important news that might have recently been released.

Corrective Arbitrage: The corrective arbitrage stage occurs when other investors exploit the consequences of source mistakes for profit. To use the above example: a separate group of savvy investors might come to realize that investors in general are failing to adequately incorporate recent news into their bids and offers. Those investors might then implement strategies to take advantage of the source mistake–e.g., they might put in place systematic plans to quickly buy up companies after they release apparent good news, selling them as their prices rise, and quickly short companies after they release apparent bad news, covering them as their prices fall.

The ability of a market to attain efficiency depends on (1) the quantity and severity of source mistakes that its investors are committing, and (2) the amount and quality of corrective arbitrage that its investors are practicing in response to those mistakes. If source mistakes are prevalent and severe, and few people are practicing corrective arbitrage in response to them, then the market will be less efficient, easier for a given active investor to beat. If, however, source mistakes are rare and insignificant, and a large portion of the market is already attempting to arbitrage them, then the market will be more efficient, harder for a given active investor to beat.

Both stages are influenced by the skill levels of participants in the market. If you raise the skill level of the participants, you will reduce the quantity and severity of source mistakes that occur, and you will increase the amount and quality of the corrective arbitrage, making the more efficient and harder to beat. If you lower the skill level of the participants, you will do the opposite, making the market less efficient and easier to beat.

With respect to the potential impact of passive investing on market efficiency, the question that matters is this: does passive investing affect the “average” skill level of the active segment of the market? In my view, the answer is yes. It increases that skill level, and therefore makes the market more efficient.

How does passive investing increase the “average” skill level of the active segment of the market? The answer: by removing lower-skilled participants, either by giving those participants a better option–i.e., the option of indexing–or nudging the wealth they’re ineptly managing into that option, putting them out of business.

In a world without indexing, uninformed investors that want exposure to a given market–e.g., retail investors that want exposure to U.S. equities, or hedge fund managers that want exposure to Brazilian equities–have to go into the market themselves and make “picks.” Either that, or they have to “pick” managers to make “picks” for them. Their “picks”–whether of individual stocks or of individual managers–are likely to be uninformed and unskilled relative to the picks of those that have experience in the market and that are doing the fundamental work necessary to know where the value is.

The option of investing in a low-cost index is impactful in that it allows investors to gain their desired exposures without having to make what would otherwise be unskilled, uninformed picks. It allows them to own the market that they want to own, without forcing them to introduce their lack of skill into the market’s active segment. In this way, it increases the average skill level of the market’s active segment, making the market more efficient, more difficult to beat.

A similar point applies to the Darwinian pressure that indexing places on active fund management businesses. The growth in indexing has to come from somewhere. Where is it most likely to come from? The answer: from actively managed funds that are consistently underperforming. If you believe in skill, then you will probably agree that those funds are more likely to lack skill than funds that are consistently outperforming. In removing them, pressuring them out of business, indexing inadvertently increases the average skill level of the active funds that remain, again making the market more difficult to beat.

It’s important to remember, here, that secondary market trading and investing is a zero-sum game for the participants. For a given market participant to outperform, some other market participant has to underperform. Obviously, for a market participant with a given level of skill, the ease at which that participant will outperform will be a function of the quantity of unskilled participants that are there for the skilled participant to exploit. To the extent that the prevalence of indexing preferentially reduces that quantity, it makes outperformance more difficult.

To summarize the point, indexing preferentially removes inexperienced, uninformed investors from the market, giving them a superior option–superior for them, because if they were to get into the fray, they would likely underperform. It also preferentially undermines the businesses of low-skill managers that fail to produce adequate results and that lose business to index competition. In this way, indexing concentrates the active share of the market into a select group of highly-skilled managers. As an active market participant, you are no longer able to do battle with low-skill participants, and are instead forced do battle with them. Think: the Bridgewaters, Third Points, Appaloosas, Bauposts, and GMOs of the world, just as examples. If you think it will be easier to outperform in a market where these entities are your primary counterparties, as opposed to a market where their presence has been diluted by a flood of run-of-the-mill managers and retail investors that don’t know what they’re doing, you’re crazy.

Now, to be clear, the increased market efficiency that comes with the growth of indexing can only manifest itself in those specific areas of the market where indexing actually becomes popular–e.g., in the U.S. large cap equity space, where a staggering 34% of all shares are being held in index funds. It’s not, however, going to manifest itself in broader areas where passive approaches remain unpopular. Investors are quite willing to gain U.S. equity exposure passively through index funds such as $SPY and $VFIAX, but they don’t seem to be willing to extend the same passive discipline to the overall universe of assets. Doing so would require them to hold stocks, bonds, and cash from around the globe in proportion to the amounts outstanding. Who wants to do that? No one, and no one is going to want to do it in the future.

Going forward, then, we should expect lower-skilled players to remain active in the broader global asset allocation game–including through the controversial practice of market timing–creating opportunities for skilled investors to outperform at their expense. If there’s a place to stay aggressively active, in my view, it’s there–in global macro–definitely not in a space like large cap U.S. equities, where the passive segment is growing literally by the day.

The Grossman-Stiglitz Paradox and the Marketplace of Ideas Fallacy

In a famous paper published in 1980, Sanford Grossman and Joseph Stiglitz introduced what is called the Grossman-Stiglitz paradox. This paradox holds that market prices cannot ever be perfectly efficient, for if they were, then investors would lack a financial incentive to do the work necessary to make prices efficient.

I want to clarify how the point that I’m making fits into this paradox. To be clear, I’m not arguing that an entire market could ever go passive. If an entire market were to go passive, there would be no transactions, and therefore no prices, and therefore no market. To have a market, someone has to actively transact–i.e., put out a bid and an offer. That someone is going to have to at least believe that there is excess profit to be had in doing so.

What passive investing does is it shrinks the portion of the market that actively transacts. It therefore shrinks the portion of the market that sets prices. But it doesn’t eliminate that portion, nor does it eliminate the profit motive that would drive that portion. It simply improves the functioning of that portion, removing the unnecessary contributions of low-skilled participants from the fray.

I anticipate that a number of economists will want to resist this claim. They will want to argue that adding lots of participants to the messy milieu of stock-picking can increase market efficiency, even if the majority of the participants being added lack skill. The problem with this view, however, is that it conceptualizes the financial market as a “marketplace of ideas”–a system where, in evolutionary fashion, different ideas are continually presented, with good ideas filtering their way the top, and bad ideas filtering out. In such a system, the introduction of diversity of any kind–even if it involves a large number of bad ideas and only a small number of good ones–has a positive effect on the final product, because the good ideas get latched onto, and the bad ideas disappear without harm.

Unfortunately, that’s not how “prices” are formed in a market. Prices are formed through the individual transactional decisions of individual people. There is no sense in which the good decisions in this lot rise to the top, nor is there any sense in which the bad decisions filter out. All of the decisions impact the price, at all times. If the average skill that underlies the decisions goes down, then so too will the quality of the ultimate product–the price.

Why Passive Indexing Makes Economies More Efficient

Imagine a world in which 500,000 individuals opt for careers in the field of active investment management. In those careers, they continually compete with each other for excess profit, setting prices for the overall market in the process. Some of the participants turn out to have skill, some turn out not to have skill–but each extracts a fee, compensation for the labor expended in the effort. The benefit that the economy gets from the arrangement is a liquid market with accurate prices.

Eventually, indexing comes around to disrupt the industry. Of the 500,000 individuals that were previously managing funds, 499,500 go out of business, with their customers choosing the passive option instead. The remaining 500–which are the absolute cream of the crop–continue to compete with each other for profit, setting prices for the overall market.

Ask yourself, what real advantage does the first arrangement have over the second? Why does an economy need to have 500,000 people arbitraging the price of $AAPL, $GOOG, $FB, and so on, when 500 of the market’s most highly-skilled active investors could do the job just as well, producing a price signal that is just as accurate, without requiring the help of the rest of the pack? There is no advantage, only the disadvantage of the lost resources.

Free markets tend to naturally correct economic inefficiences. To have a very large number of highly-talented people duplicating each other’s arbitrage efforts is an inefficiency, particularly in secondary markets where the actual physical capital that underlies the securities has already been formed and will not be affected by the market price. Passive management represents its inevitable solution.

Conclusion: Can It Make Sense to Invest in an Active Manager?

We conclude the piece with the question: can it make sense to invest with an active manager? If by “active manager” we’re talking about a financial advisor, then the answer is obviously yes. A financial advisor can help otherwise financially uninformed clients avoid mistakes that have the potential to be far more costly than the fees charged, particularly if the fees charged are reasonable. They can also improve clients’ state of mind, by allowing clients to offload stressful decisions onto a trusted expert. But I’m directing the question more towards active fund managers–active stock-pickers that are trying to deliver better exposures to the market than an index fund can offer. Can it make sense to invest with those managers? In my view, the answer is also yes.

An analogy is helpful here. Like secondary-market investing, law is a zero-sum game. If you aggregate the individual performances of all civil attorneys, and you exclude cases where multiple attorneys work together in cases, the average win percentage of any given attorney will be 50%–in other words, average. Does it follow that if you could eliminate fees by using an “average” attorney, that you should do so? No, not at all. The legal universe as a whole cannot do better than the average attorney, and so if the universe of litigants as a whole can avoid fees in the conduct of its zero-sum business, then it should. But you, yourself, considered as an individual litigant seeking a claim in your favor, are not the universe of litigants. It’s perfectly conceivable that you–considered strictly as an individual case–might have the ability to find an attorney that is better than average. If you have that ability, then settling for the average would be foolish, especially if you have lot at stake.

With respect to a legal case, what you need to ask yourself is this: do you believe that you have the insight into attorney skill to pick an attorney that is better than the average attorney–and not only better, but better by an amount sufficient to justify the fees that you will have to pay for the service? Maybe, maybe not. It depends on how good you are at identifying legal skill, and on how much your preferred attorney wants to charge you. Depending on the price, betting on that attorney’s skill may be worth it.

The same is true in the arena of investing. Do you believe that you have the insight necessary to identify an active manager whose skill exceeds that of the aggregate market? More importantly, does your manager’s excess skill level, and the excess returns that will come from it, justify the fees that she’s going to charge? If the fees are north of 200 bps, then, in my view, with the exception of a select group of highly talented managers, the answer is no. Modern markets are reasonably efficient, and difficult to consistently beat. There are investors with the skill to beat them, but only the select few can do it consistently, and even fewer by such a large amount.

At the same time, many managers charge much lower fees–some as low as 50 bps, which is only 35 bps more than the typical passive fund. That differential–35 bps–is almost too small to worry about, even when stretched out over long periods of time. In my view, there are a number of active managers and active strategies that can justify it.

The downturn in the energy sector and persistent economic weakness abroad has caused the investment community to become increasingly focused on the possibility of a U.S. recession. In this piece, I’m going to examine a historically powerful indicator that would seem to rule out that possibility, at least for now.

The following chart (source: FRED) shows the seasonally-adjusted U.S. civilian unemployment rate (UE) from January 1948 to January 2016:

As the chart illustrates, the unemployment rate is a lagging indicator of recession. By the time high unemployment takes hold in an economy, a recession has usually already begun.

In contrast with the absolute level, the trend in the unemployment rate–the direction that the rate is moving in–is a coincident indicator of recession, and can sometimes even be a leading indicator. As the table below shows, in each of the eleven recessions that occurred since 1948, the trend in the unemployment rate turned higher months before the recession began. The average lead for the period was 3.45 months.

Admittedly, the phrase “turning higher” is ambiguous. We need to be more precise, and so we’re going to define the phrase in terms of trailing moving averages. That is, we’re going to say that the unemployment rate trend has turned higher whenever its current value crosses above the moving average of its trailing values over some period, and that the unemployment rate trend has turned lower whenever its current value falls below the average of its trailing values over some period.

In the following chart, we plot the unemployment rate alongside its trailing 12 month moving average from January 1948 to January 2016. The red and green circles delineate important crossover points, with red crossovers delineating upward (bearish) turns, and green crossovers delineating downward (bullish) turns:

As you can see, historically, whenever the unemployment rate has crossed above the moving average, a recession has almost always followed shortly thereafter. Similarly, for every recession that actually did occur in the period, the unemployment rate successfully foreshadowed the recession in advance by crossing above its moving average.

The following chart takes the indicator back farther, from April 1929 to April 1947:

In contrast with the earlier chart, the indicator here appears to be a bit late. After capturing the onset of the Great Depression almost perfectly, the indicator misses the onset of the 1937 and 1945 recessions by a few months. It’s not alone in that respect–the 1937 and 1945 recessions were missed by pretty much every other recession indicator on the books.

The Fed is well aware of the recession forecasting power of the trend in the unemployment rate. New York Fed president William Dudley discussed the matter explicitly in a speech just last month:

“Looking at the post-war period, whenever the unemployment rate has increased by more than 0.3 to 0.4 percentage points, the economy has always ended up in a full-blown recession with the unemployment rate rising by at least 1.9 percentage points. This is an outcome to avoid, especially given that in an economic downturn the last to be hired are often the first to be fired. The goal is the maximum sustainable level of employment—in other words, the most job opportunities for the most people over the long run.”

As far as the U.S. economy is concerned, the indicator’s current verdict is clear: no recession. We may enter a recession later this year, or next year, but we’re not in a recession right now.

Individual energy-exposed regions of the country, however, are in recession, and the indicator is successfully flagging that fact. The following chart shows the unemployment rate for Houston (source: FRED):

Per the indicator, Houston’s economy is solidly in recession. We know the reason why: the plunge in oil prices.

Dallas is tilting in a similar direction. But it’s a more diversified economy, with less exposure to oil and gas production, so the tilt isn’t as strong (source: FRED):

If the larger U.S. economy is not in a recession, what is the investing takeaway? The takeaway is that we should be constructive on risk, with a bias towards being long equities, given the reduced odds of a large market drop. Granted, recessions aren’t the only drivers of large market drops, but they’re one of the few drivers that give clear signs of their presence before the drops happen, so that investors can get out of the way. Where they can be ruled out, the risk-reward proposition of being long equities improves dramatically.

Now, the rest of this piece will be devoted to an rigorous analysis of the unemployment rate trend as a market timing indicator. The analysis probably won’t make sense to those readers that haven’t yet read the prior piece on “Growth-Trend Timing”, so I would encourage them to stop here and go give it a skim. What I say going forward will make more sense.

To begin, recall that GTT seeks to improve on the performance of a conventional trend-following market timing strategy by turning off the trend-following component of the strategy (i.e., going 100% long no matter what) during periods where the probability of recession is low. In this way, GTT avoids substantial whipsaw losses, while incurring only a slightly increased downside risk.

Using the unemployment rate as an input, the specific trading rule for GTT would be:

(1) If the unemployment rate trend is downward, i.e., not indicating an oncoming recession, then go 100% long U.S. equities.

(2) If the unemployment rate trend is upward, indicating an oncoming recession, then defer to the price trend. If the price trend is upward, then go 100% long U.S. equities. If the price trend is downward, then go to cash.

To summarize, GTT will be 100% invested in the market unless the unemployment rate trend is upward at the same time that the price trend is downward. Together, these indicators represent a double confirmation of danger that forces the strategy to take a safe position.

The following chart shows the strategy’s performance in U.S. equities from January 1930 to January 2016. The unemployment rate trend is measured in terms of the position of the unemployment rate relative to its trailing 12 month moving average, where above signifies an upward trend, and below signifies a downward trend. The price trend is measured in a similar way, based on the position of the market’s total return index relative to the trailing 10 month moving average of that index:

The blue line is the performance of the strategy, GTT. The green line is the performance of a pure and simple moving average strategy, without GTT’s recession filter. The dotted red line is the outperformance of GTT over the simple moving average strategy. The yellow line is a rolled portfolio of three month treasury bills. The gray line is buy and hold. The black line is GTT’s “X/Y” portfolio–i.e., a portfolio with the same net equity and cash exposures as GTT, but achieved through a constant allocation over time, rather than through in-and-out timing moves (see the two prior pieces for a more complete definition). The purple bars indicate periods where the unemployment rate trend is downward, ruling out recession. During those periods, the moving average strategy embedded in GTT gets turned off, directing the strategy to take a long position no matter what.

As the chart illustrates, the strategy beats buy and hold (gray) as well as a simple moving average (green) strategy by over 150 basis points per year. That’s enough to triple returns over the 87 year period, without losing any of the moving average strategy’s downside protection.

We can add a seventh input to the group: the unemployment rate trend (UE vs. 12 MMA). The following table shows GTT’s excess performance over a simple moving average strategy on each of the seven inputs, taken individually:

As the table shows, the unemployment rate trend beats all other inputs. To understand why it performs better, we need to more closely examine what GTT is trying to accomplish.

Recall that the large market downturns that drive the outperformance of trend-following strategies tend to happen in conjunction with recessions. When a trend-following strategy makes a switch that is not associated with an ongoing or impending recession, it tends to incur whipsaw losses. (Note: these losses were explained in thorough detail in the prior piece).

What GTT tries to do is use macroeconomic data to distinguish periods where a recession is likely from periods where a recession is unlikely. In periods where a recession is unlikely, the strategy turns off its trend-following component, taking a long position in the market no matter what the price trend happens to be. It’s then able to capture the large downturns that make trend-following strategies profitable, without incurring the frequent whipsaw losses that would otherwise detract from returns.

The ideal economic indicator to use in the strategy is one that fully covers the recessionary period, on both sides. The following chart illustrates using the 2008 recession as an example:

We want the red area, where the recession signal is in and where the trend-following component is turned on, to fully cover the recessionary period, from both ends. If the signal comes in early, before the recession begins, or goes out late, after the recession has ended, the returns will not usually be negatively impacted. The trend-following component of the strategy will take over during the period, and will ensure that the strategy profitably trades around the ensuing market moves.

What we categorically don’t want, however, is a situation where the red area fails to fully cover the recessionary period–in particular, a situation where the indicator is late to identify the recession. If that happens, the strategy will not be able to exit the market on the declining trend, and will risk of getting caught in the ensuing market downturn. The following chart illustrates the problem using the 1937 recession as an example:

As you can see, the indicator flags the recession many months after it has already begun. The trend-following component therefore doesn’t get turned on until almost halfway through the recessionary period. The risk is that during the preceding period–labeled the “danger zone”–the market will end up suffering a large downturn. The strategy will then be stuck in a long position, unable to respond to the downward trend and avoid the losses. Unfortunately for the strategy, that’s exactly what happened in the 1937 case. The market took a deep dive in the early months of the recession, before the indicator was flagging. The strategy was therefore locked into a long position, and suffered a large drawdown that a simple unfiltered trend-following strategy would have largely avoided.

We can frame the point more precisely in terms of two concepts often employed in the area of medical statistics: sensitivity and specificity. These concepts are poorly-named and very easy to confuse with each other, so I’m going to carefully define them.

The sensitivity and specificity of an indicator are defined as follows:

Sensitivity: the percentage of actual positives that the indicator identifies as positive.

Specificity: the percentage of actual negatives that the indicator identifies as negative.

To use an example, suppose that there are 100 recessionary months in a given data set. In 86 of those months, a recessionary indicator comes back positive, correctly indicating the recession. The indicator’s sensitivity to recession would then be 86 / 100 = 86%.

Alternatively, suppose that there are 700 non-recessionary months in a given data set. In 400 of those non-recessionary months, a recessionary indicator comes back negative, correctly indicating no recession. The indicator’s specificity to recession would then be 400 / 700 = 57%.

More than anything else, what GTT needs is an indicator with a high sensitivity to recession–an indicator that rarely gives false negatives, and that will correctly indicate that a recession is happening whenever a recession is, in fact, happening.

Having a high specificity to recession, in contrast, isn’t as important to the strategy, because the strategy has the second layer of the price trend to protect it from unnecessary switches. If the indicator sometimes overshoots with false positives, indicating a recession when there is none, the strategy won’t necessarily suffer, because if there’s no recession, then the price trend will likely be healthy. The healthy price trend will keep the strategy from incorrectly exiting the market on the indicator’s mistake.

Of all the indicators in the group, the unemployment rate trend delivers the strongest performance for GTT because it has the highest recession sensitivity. If there’s a recession going on, it will almost always tell us–better than any other single recession indicator. In situations where no recession is happening, it may give false positives, but that’s not a problem, because unless the false positives coincide with a downward trend in the market price–an unlikely coincidence–then the strategy will stay long, avoiding the implied whipsaw.

For comparison, the following tables show the sensitivity and specificity of the different indicators across different time periods:

As the tables confirm, the unemployment rate has a very strong recession sensitivity, much stronger than any other indicator. That’s why it produces the strongest performance.

Now, we can still get good results from indicators that have weaker sensitivities. We just have to aggregate them together, treating a positive indication from any of them as a positive indicatation for the aggregate signal. That’s what we did in the previous piece. We put real retail sales growth and industrial production growth together, housing start growth and real personal income growth together, and so on, increasing the sensitivity of the aggregate signal at the expense of its specificity.

Right now, only two of the seven indicators are flagging recession: industrial production growth and total return EPS growth. We know why those indicators are flagging recession–they’re getting a close-up view of the slowdown in the domestic energy sector and the unrelated slowdown in the larger global economy. Will they prove to be right? In my view, no. Energy production is a small part of the US economy, even when multipliers are considered. Similarly, the US economy has a relatively low exposure to the global economy, even though a significant portion of the companies in the S&P 500 are levered to it.

Even if we decide to go with industrial production growth (or one of its ISM siblings) as the preferred indicator, recent trends in that indicator are making the recession call look shakier. In the most recent data point, the indicator’s growth rate has turned up, which is not what we would expect to be seeing right now if the indicator were right and the other indicators were wrong:

Now, the fact that a U.S. recession is unlikely doesn’t mean that the market is any kind of buying opportunity. Valuation can hold a market back on the upside, and the market’s current valuation is quite unattractive. At a price of 1917, the S&P 500’s trailing operating P/E ratio is 18.7. Its trailing GAAP P/E ratio is 21.5. Those numbers are being achieved on peaking profit margins–leaving two faultlines for the market to crack on, rather than just one. Using non-cyclical valuation measures, which reflect both of those vulnerabilities, the numbers get worse.

My view is that as time passes, the market will continue to acclimatize to the two issues that it’s been most worried about over the last year: (1) economic weakness and potential instability in China and (2) the credit implications of the energy downturn. A similar acclimatization happened with the Euro crisis. It always seems to happen with these types of issues. The process works like this. New “problems” emerge, catching investors off-guard. Many investors come to believe that this is it, the start of the “big” move lower. The market undergoes a series of gyrations as it wrestles with the problems. Eventually, market participants get used to them, accustomed to their presence, like a swimmer might get accustomed to cold water. The sensitivity, fear and reactivity gradually dissipate. Unless the problems continue to deteriorate, investors gravitate back into the market, even as the problems are left “unsolved.”

Right now, there’s a consensus that an eventual devaluation of the yuan, with its attendant macroeconomic implications, is itself a “really bad thing”, or at least a consequence of a “really bad thing” that, if it should come to pass, will produce a large selloff in U.S. equities. But there’s nothing privileged or compelling about that consensus, no reason why it should be expected to remain “the” consensus over time. If we keep worrying about devaluations, and we don’t get them, or we do get them, and nothing bad happens, we will eventually grow less concerned about the prospect, and will get pulled back into the market as it grinds higher without us. In actuality, that seems to be what’s already happening.

Valuation-conscious investors that are skeptical of the market’s potential to deliver much in the way of long-term returns–and I would include myself in that category–do have other options. As I discussed in a piece from last September, we can take advantage of elevated levels of volatility and sell puts or covered calls on a broad index such as the S&P 500 or the Russell 2000. By foregoing an upside that we do not believe to be attractive to begin with, we can significantly pad our losses in a potential downturn, while earning a decent return if the market goes nowhere or up (the more likely scenario, in my view).

To check in on the specific trade that I proposed, on September 6th, 2015, with $SPY at 192.59, the bid on the 165 September 2016 $SPY put was 8.79. Today, $SPY is at essentially the same price, but the value of the put has decayed substantially. The ask is now 4.92. On a mark-to-market basis, an investor that put a $1,000,000 into the trade earned roughly $4 per share–$24,000, or roughly 6% annualized, 6% better than the market, which produced nothing.

For the covered call version of the trade, the bid on the 165 September 2016 call was 33.55. As of Friday, the ask is now 30.36. On a mark-to-market basis, then, the investor has earned roughly $3.20 in the trade. The investor also pocketed two $SPY dividends, worth roughly $2.23. In total, that’s $5.43 per share, or roughly 8% annualized. If the market continues to churn around 1900, the investor will likely avoid assignment and get to stay in the trade, if not through both of the upcoming dividends, then at least through the one to be paid in March.

To summarize, right now, the data is telling us that a large, recessionary downturn is unlikely. So we want to be long. At the same time, the heightened state of valuations and the increasing age of the current cycle suggest that strong returns from here are unlikely. In that kind of environment, it’s attractive to sell downside volatility. Of course, in selling downside volatility, we lose the ability to capitalize on short-term trading opportunities. Instead of selling puts last September, for example, we could have bought the market, sold it at the end of the year at the highs, and then bought it back now, ready to repeat again. But that’s a difficult game to play, and an even more difficult game to win at. For most of us, a better approach is to identify the levels that we want to own the market at, and get paid to wait for them.

While we’re on the topic of GTT and recession-timing, I want to address a concern that a number of readers have expressed about GTT’s backtests. That concern pertains to the impact of data revisions. GTT may work well with the revised macroeconomic data contained in FRED, but real-time investors don’t have access to that data–all they have access to is unrevised data. But does the strategy work on unrevised data?

Fortunately, it’s possible (though cumbersome) to access unrevised data through FRED. Starting with the unemployment rate, the following chart shows the last-issue revised unemployment rate alongside the first-issue unrevised unemployment rate from March 1961 to present:

As you can see, there’s essentially no difference between the two rates. They overlap almost perfectly, confirming that the revisions are insignificant.

Generally, in GTT, the impact of revisions is reduced by the fact that the strategy pivots off of trends and year-over-year growth rates, rather than absolute levels and monthly growth rates, where small changes would tend to have a larger effect.

The following chart shows the performance of GTT using from March 1961 to present using first-issue unrevised unemployment rate data (orange) and last-issue revised unemployment rate data (blue). Note that unrevised data prior to March 1961 is not available, which is why I’ve chosen that date as the starting point:

Interestingly, in the given data set, the strategy actually works better on unrevised data. Of course, that’s likely to be a random occurrence driven by luck, as there’s no reason for unrevised data to produce a superior performance.

The following chart shows the performance of GTT using available unrevised and revised data for industrial production growth back to 1928:

In this case, the strategy does better under the revised data, even though both versions outperform the market and a simple moving average strategy. The difference in performance is worth about 40 basis points annually, which is admittedly significant.

One driver of the difference between the unrevised and revised performance for the industrial production case is the fact that the unrevised data produced a big miss in late 2011, wrongly going negative and indicating recession when the economy was fine. Recently, a number of bearish commentators have cited the accuracy of the industrial production growth indicator as a reason for caution, pointing out that the indicator that has never produced sustained negative year over year growth outside of recession. That may be true for revised data, but it isn’t true for unrevised data, which is all we have to go on right now. Industrial production growth wrongly called a recession in 2011, only to get revised upwards several months later.

The following chart shows the performance of GTT using available unrevised and revised data for real retail sales growth:

The unrevised version underperforms by roughly 20 basis points annually.

The following chart shows the performance of GTT using available unrevised and revised data for job growth:

For job growth, the two versions perform about the same.

Combining indicators shrinks the impact of inaccuracies, and reduces the difference between the unrevised and revised cases. The following chart illustrates, combining industrial production and job growth into a single “1 out of 2” indicator:

Unfortunately, unrevised data is unavailable for EPS (the revisions would address changes to SEC 10-Ks and 10-Qs), real personal income growth, and housing start growth. But the tests should provide enough evidence to allay the concerns. The first-issue data, though likely to be revised in small ways, captures the gist of what is happening in the economy, and can be trusted in market timing models.

In a future piece, I’m going to examine GTT’s performance in local currency foreign equities. GTT easily passes out-of-sample testing in credit securities, different sectors and industries, different index constructions (where, for example, the checking days of the month are chosen randomly), and individual securities (which simple unfiltered trend-following strategies do not work in). However, the results in foreign securities are mixed.

If we use U.S. economic data as a filter to time foreign securities, the performance turns out to be excellent. But if we use economic data from the foreign countries themselves, then the strategy ends up underperforming a simple unfiltered trend-following strategy. Among other things, this tells us something that we could probably have already deduced from observation: the health of our economy and our equity markets is more relevant to the performance of foreign equity markets than the health of their own economies. This is especially true with respect to large downward moves–the well-known global “crises” that drag all markets down in unison, and that make trend-following a historically profitable strategy.